TRIGONOMETRY QUESTIONS
1.What is the value of
tan(25∘)+tan(50∘)1−tan(25∘)×tan(50∘)tanθ(25∘)+tanθ(50∘)1−tanθ(25∘)×tanθ(50∘)
A. 2+3–√2+3
B. 1+23–√1+23
C. 2+13–√2+13
D. 1+3–√2+3
Solution: Option(A) is correct
We know the addition formula for the tangent,
tan(A+B)=tan(A)+tan(B)1−tan(A)×tan(B)tan(A+B)=tan(A)+tan(B)1−tan(A)×tan(B)
Thus,
tan(25∘)+tan(50∘)1−tan(25∘)×tan(50∘)tanθ(25∘)+tanθ(50∘)1−tanθ(25∘)×tanθ(50∘)
=tan(25∘+50∘)=tan(25∘+50∘)
=tan(75∘)=tan(75∘)
=tan(45∘+30∘)=tan(45∘+30∘)
=tan(45∘)+tan(30∘)1−tan(45∘)×tan(30∘)=tanθ(45∘)+tanθ(30∘)1−tanθ(45∘)×tanθ(30∘)
=1+13–√1−(1×13–√)=1+131−(1×13)
=2+3–√2+3
2. If (2 sin θ-cos θ)/(cos θ+sin θ)=1, then the value of cot θ is
A. 1/2
B. 1/3
C. 3
D. 2
Sol: Correct Option: A
Dividing numerator and denominator by sin θ
⇒ [(2 sin θ – cos θ)/sin θ] / [(cos θ + sin θ)/sin θ] = 1
⇒ (2– cot θ)/(1 + cot θ)= 1
⇒ 2 – cot θ = 1 + cot θ
⇒ cot θ = 1/2
Hence, option A is correct.
3. If cot (Π/2 – θ) = √3,then the value of cos θ is
A. 0
B. 1/√2
C. 1/2
D. 1
Correct Option: C
cot (Π/2– θ)= √3
⇒ tan θ = √3
[∵ cot (Π/2– θ ) = tan θ ]
∴ θ = 60°
Hence, cos 60° = 1/2.
Therefore, the right option is C.
4. The value of sin (45° + θ) – cos (45° – θ) is
A. 1
B. 0
C. 2 cos θ
D. 2 sin θ
Correct Option: B
sin(45° + θ) – cos(45° – θ)
= sin{90° – (45° – θ)} – cos (45° – θ)
= cos (45° – θ) – cos (45° – θ)
{∵sin(90 – A) = cos A }
= 0
Hence, option B is correct.
5. If tan4θ + tan2θ = 1, then the value of cos4θ + cos2θ is
A. 8
B. 10
C. 1
D. 2
Correct Option: C
tan4θ + tan2θ = 1
tan2θ (tan2θ + 1)
⇒ tan2θ. sec2θ = 1 {∵ sec2θ = 1 + tan2θ}
⇒ (sin2θ)/(cos4θ)= 1
⇒ 1– cos2θ = cos4 θ {∵ sin2 θ = 1 – cos2θ}
⇒ cos4 θ + cos2 θ = 1
Hence, option C is correct.
6. Find the value of sin2 10 + sin2 20 + sin2 30 + ....... + sin2 80.
A. 2
B. 3
C. 1
D. 4
Correct Option: D
We can rewrite above equation as
sin2 10 + sin2 80 + sin2 20 + sin2 70 + sin2 30 + sin2 60 + sin2 40 + sin2 50 ….. equation (A)
We know that sin2 x + sin2 (90 – x) = 1
Therefore equation A becomes
1 + 1 + 1 + 1 = 4
Hence, option D is correct.
7. Find the value of
cos2 Θ ({√1 + sin Θ}/{√1 – sin Θ}+ {√1 – sin Θ}/{√1 + sin Θ})
A. cos Θ
B. cos Θ/2
C. 2 cosΘ
D. √2 cos Θ
Correct Option: C
cos2 Θ ([√ (1 + sin Θ) (1 + sin Θ)/√ (1 – sin Θ) (1 + sin Θ)]+[√ (1 – sin Θ) (1 – sin Θ)/√ (1 + sin Θ) (1 – sin Θ)])
⇒ cos2 Θ ([√ ((1 + sin Θ)2)/√ ((1 – sin2 Θ))]+ [√ (1 – sin Θ)2/√ (1 – sin2 Θ)])
⇒ cos2 Θ ([{√ (1 + sin Θ)2}/√cos2 Θ] + [{√ (1 – sin Θ)2}/√cos2 Θ])
⇒ cos2 Θ ((1 + sin Θ)/cos Θ + (1 – sin Θ)/cos Θ )
⇒ cos2 Θ ((1 + sin Θ + 1 – sin Θ)/cos Θ)
2 cos2 Θ/cos Θ = 2 cos Θ
Hence, option C is correct.
8. Find the value of :
(sin 35°/cos 55°)2+ (cos 55°/sin 35°)2 – 2 cos 30°
A. 0
B. 1 – √3
C. 2 – √3
D.3
Correct Option: C
(sin 35°/cos 55°)2+ (cos 55°/sin 35°)2 – 2 cos 30°
⇒ (sin (90 – 35°)/cos 55°)2+ (cos (90 – 55°)sin 35° )2– 2 cos 30°
⇒ (cos 55 °/cos 55°)2+ (sin 35°/sin 35°)2– 2 cos 30°
⇒ 1 + 1 – 2 × (√3/2)
⇒ 2 – √3
Hence, option C is correct.
9. Evaluate the expression sin4 x + cos4 x when x = pi/4
A. (1/2)
B. -1
C. -2
D. (3/2)
E. None of these
Correct Ans:-1
10. Find the sum of all the angles (in degrees) if the polygon has 10 sides.
A. 1452
B. 1443
C. 1440
D. 1442
E. None of these
Correct Ans:1440
11. If tan(10x - 20) = cot(10y+30) then find the value of x + y.
A. 8
B. 16
C. 13
D. 11
E. None of these
Correct Ans:8
12. Find the sum of all the angles (in degrees) if the polygon has 11 sides.
A. 1625
B. 1630
C. 1825
D.1620
E. None of these
Correct Ans:1620
Given, number of sides of a polygon, n = 11
Sum of all angles of polygon = (2n – 4) * right angles
= (2*11 – 4) * 90
= (22 – 4) * 90
= 18 * 90
= 1620
Sum of all angles of polygon = 1620
13. Find the sum of all the angles (in degrees) if the polygon has 16 sides.
A. 2530
B. 2520
C. 2526
D. 2527
E. None of these
Correct Ans:2520
Given, the sides of polygon (n) = 16
Sum of all the angles (in degrees) = (n – 2) * 180
= (16 – 2) * 180
= 14 * 180
= 2520
14. Evaluate the area of the triangle if a = 7, b = 36 and angle C = 90.
A. 125
B. 122
C. 124
D. 126
E. None of these
Correct Ans:126
Given, for triangle, a = 7, b = 36 and angle C = 90
Area of triangle = (a * b * sin C) / 2
= (7 * 36 * sin 90) / 2
Since, sin 90 = 1
=> Area of triangle = (7 * 36 * 1) / 2
=> Area of triangle = 126
15. Evaluate: sin(20) cos(70)+sin(70) cos (20)
A. 0
B. -1
C. 1
D.cos(50)
E. None of these
Correct Ans:1
By the Formula:
sin A cos B + cos A sin B = sin (A + B)
Here, A = 20 and B = 70
sin (20) cos (70) + cos(20) sin (70) = sin (20 + 70)
= sin (90)
= 1 (since, value of sin 90 = 1)
Thus, sin (20) cos (70) + cos(20) sin (70) = 1
16. Evaluate: sin(17) cos(73)+sin(73) cos (17)
A. 0
B. 1
C. sin(56)
D. cos(56)
E. None of these
Correct Ans:1
Given expression is: sin(17) cos(73)+sin(73) cos (17)
By the Formula:
sin A cos B + cos A sin B = sin (A + B)
Here, A = 17 and B = 73
=> sin(17) cos(73)+sin(73) cos (17) = sin (17 + 73)
= sin (90)
= 1
Thus, sin(17) cos(73)+sin(73) cos (17) = 1
17. Evaluate the area of the triangle if a = 7, b = 12 and angle C = 90.
A. 44
B. 45
C. 46
D. 42
E. None of these
Correct Ans:42
Given, a = 7, b = 12
Angle C = 90
Area of triangle = ab sin (angle C) / 2
= 7 * 12 * sin (90) / 2
= 7 * 6 * sin (90)
= 42 * sin (90)
Since, sin (90) = 1
=> Area of triangle = 42 * 1 = 42
Therefore, Area of triangle = 42
18. Evaluate: sin(21) cos(69)+sin(69) cos (21)
A. 1
B. -1
C. sin(48)
D. cos(48)
E. None of these
Correct Ans:1
By using Formula:
Sin a cos b + cos a sin b = sin (a + b)
Let a = 21, b = 69
=> Sin (21) cos (69) + cos (21) sin (69) = sin (21 + 69)
= sin (90)
= 1
Therefore, sin(21) cos(69)+sin(69) cos (21) = 1
19. sin2 20° + sin2 70° - tan2 45° = ?
A. 2
B. 0
C. 1
D. 1/2
E. None of these
Correct Ans:0
sin2 20° + sin2 70° - tan2 45° = ?
=> sin2 (90° - 70°) + sin2 70° - 12 (Since tan 45° = 1)
=> cos2 70° + sin2 70° - 1
=> 1 -1 = 0
20. If sinθ = 8/17, then secθ is equal to
A. 15/17
B. 17/15
C. 18/15
D. 15/18
E. None of these
Correct Ans:17/15
Given, sinθ = 8/17
WKT, sinθ = opp/hyp
Therefore, opp/hyp = 8/17
secθ = 1/cosθ
cosθ = adj/hyp
Since, (hyp)2 = (opp)2 + (adj)2
(adj)2 = (hyp)2 - (opp)2
(adj)2 = (17)2 - (8)2
(adj)2= 289 - 64
(adj)2 = 225
adj = 15
Therefore, cosθ = 15/17
secθ = 1/(15/17) = 17/15
21. What is the value of (1/√3) + cos 60º
A. (2 + 2√3)/√3
B. (2 + √3)/2√3
C. 7/3
D. (√2 + 1)/√2
E. None of these
Correct Ans:(2 + √3)/2√3
We know that,
Cos 60º = 1/2
(1/√3) + cos 60º = (1/√3) + (1/2)
= (2 + √3)/2√3
22. Evaluate the area of the triangle if a = 4, b = 8 and angle C = 60
A. 15.92
B. 13.92
C. 17.92
D. 14.92
E. None of these
Correct Ans:13.92
Given, for triangle, a = 4, b = 8 and angle C = 60
Area of triangle = (a * b * sin C) / 2
= (4 * 8 * sin 60) / 2
= 16 * sin 60
Since, sin 60 = sqrt(3) / 2
=> Area of triangle = 16 * [sqrt(3) / 2]
=> Area of triangle = 8 * sqrt(3)
=> Area of triangle = 13.92
23. Evaluate the area of the triangle if a = 3, b = 12 and angle C = 45.
A. 12.78
B. 15.78
C. 16.78
D. 13.78
E. None of these
Correct Ans:12.78
Given, a = 3, b = 12
Angle C = 45
Area of triangle = ab sin (angle C) / 2
= 3 * 12 * sin (45) / 2
= 3 * 6 * sin (45)
= 18 * sin (45)
Since, sin (45) = 1/sqrt(2) = 1/1.414
=> Area of triangle = 18 * [1/1.414]
= 12.73
Therefore, Area of triangle = 12.73
24. If sin x + cos x = a, then a^2 - 1 = ?
A. 2 sin x + cos x
B. 2 sin x cos x
C. sin x cosx
D. 2 sin x - cos x
E. None of the above
Correct Ans: 2 sin x cos x
Given, sin x + cos x = a
Then, a^2 – 1 = (sin x + cos x)^2 – 1
=> a^2 – 1 = sin^2 x + cos^2 x + 2sin x.cos x -1
Since, sin^2 x + cos^2 x =1
=> a^2 – 1 = 1 + 2sin x.cos x -1
=> a^2 – 1 = 2sin x.cos x
25. If sin x = 4 /5 then evaluate cosec^2 (x) - cot^2 (x) = ?
A. 1/2
B. 1
C. -1
D. 0
E. None of the above
Correct Ans:1
We know the Trigonometric identity:
1 + cot^2 x = cosec^2 x
=> cosec^2 x - cot^2 x = 1
26. If cos x = 1 then evaluate tan^3x + tanx = ?
A. 3
B. 1
C. 4
D. 0
E. None of the above
Correct Ans:0
Given, cos x = 1
Squaring on both sides, we get
=> cos^2 x = 1
=> 1 - cos^2 x = 0
Since sin^2 x + cos^2 x = 1 ---->1 - cos^2 x = sin^2 x
=> sin^2 x = 0
=> sin x = 0
Then, tan^3 x + tan x = (sin x / cos x)^3 + (sin x / cos x)
On substituting, sin x = 0 and cos x = 1 in the above eqn, we get
=> tan^3 x + tan x = (0/1)^3 + (0/1)
=> tan^3 x + tan x = 0
27. If sin x = 1, then cos^4 x + cos^2 x = ?
A. 2
B. sqrt(2)
C. 1
D. 0
E. None of the above
Correct Ans:0
Given, sin x = 1
Now, cos^2 x = 1 – sin^2 x
=> cos^2 x = 1 – (1)^2
=> cos^2 x = 1 – 1
=> cos^2 x = 0
Now, cos^4 x = (cos^2 x)^2
=> cos^4 x = (0)^2
=> cos^4 x = 0
Therefore, cos^4 x + cos^2 x = 0
28. Find the minimum value of 3 sin (x+16) + 4 cos (x+16)
A. 1
B. -1
C. -5
D. 3
E. None of the above
Correct Ans:-5
Given expression: 3 sin (x+16) + 4 cos (x+16)
Minimum value of A sin x + B cos x = - sqrt(A^2 + B^2)
=> Minimum value of 3 sin (x+16) + 4 cos (x+16)= - sqrt(3^2 + 4^2)
= -sqrt(9+16)
= - sqrt(25)
= -5
Thus, Minimum value of 3 sin (x+16) + 4 cos (x+16)= -5
29. Which of the following expressions is equivalent to sin 6x :
A. sin 2x cos 4x - cos 4x sin 2x
B. sin 2x cos 4x + cos 2x sin 4x
C. sin 2x + cos (4x)
D. sin 2x + sin 4x
E. None of the above
Correct Ans:sin 2x cos 4x + cos 2x sin 4x
sin (A + B) = sin A cos B + cos A sin B
Let A = 2x and B = 4x
Sin (6x) = sin (2x + 4x) = sin (2x) cos (4x) + cos (2x) sin (4x)
30. If a and b denote the maximum and minimum value of the expression 3 sin x + 2 cos x, then a + b = ?
A. 5
B. 1
C. 0
D. -1
E. None of the above
Correct Ans:0
Given “a” and “b” denote maximum and minimum value of the expression: 3 sin x + 2 cos x
Formulae used:
Maximum value of A sin x + B cos x = +sqrt(A^2 + B^2)
Minimum value of A sin x + B cos x = - sqrt(A^2 + B^2)
So, a = Maximum value of 3 sin x + 2 cos x
=> a = sqrt(3^2 + 2^2)
=> a = sqrt(13)
=> a = 3.6
b = Minimum value of 3 sin x + 2 cos x
=> b = - sqrt(3^2 + 2^2)
=> b = -3.6
Now, a + b = 3.6 – 3.6 = 0
31. If sin x + cosec x = 2 , then sin ^3 x + cosec^3 x = ?
A. 1
B. 1/2
C. 8
D. 2
E. None of the above
Correct Ans:2
Given, sin x + cosec x = 2
=> sin x + (1/ sin x) = 2 ---> (Since, cosec x = 1/ sin x)
On taking L.C.M, we get
Sin ^2 x + 1 = 2 sin x
=> Sin ^2 x - 2 sin x + 1 = 0
By the formula: a^2 – 2ab + b^2 = (a – b)^2
=> (sin x – 1)^2 = 0
=> sin x – 1 = 0
=> sin x = 1
sin ^3 x + cosec^3 x = sin ^3 x + (1/ sin ^3 x)
= 1 + (1/1)
= 2
Thus, sin ^3 x + cosec^3 x = 2
32. Which of the following option represents the sides of a right angled triangle?
A. 3 ,4 , 6
B. 4 , 5 , 6
C. 11,60 , 71
D. 11, 60, 61
E. None of these
Correct Ans:11, 60, 61
For right angled triangle,
Hypotenuse side (largest side) = sqrt(sum of other two sides)
From among the given options
=> 61 = sqrt (11^2 + 60^2)
=> 61 = sqrt(121 + 3600)
=> 61 = sqrt(3721)
=> 61 = 61
Thus 11, 60, 61 forms a right angled triangle.
33. If 5 sin x + 5 cos x = m and 5 cos x - 5 sin x = n, then find the value of m^2 + n^2.
A. 50
B. 52
C. 53
D. 54
E. None of these
Correct Ans: 50
Given, m = 5 sin x + 5 cos x
Then m2 = (5 sin x + 5 cos x)2
=> m2 = 52(sin x + cos x)2
=> m2 = 25 (sin2 x + cos2 x + 2 sin x.cos x)
Since sin2 x + cos2 x = 1
=> m2 = 25 (1 + 2 sin x.cos x)
Given, n = 5 cos x - 5 sin x
Then, n2 = (5 cos x - 5 sin x)2
=> n2 = 52 (cos x – sinx)2
=> n2 = 25 (cos2 x + sin2 x – 2 sinx.cos x)
Since sin2 x + cos2 x = 1
=> n2 = 25 (1 – 2 sinx.cos x)
Now m2 + n2 = 25 (1 + 2 sin x.cos x) + 25 (1 – 2 sinx.cos x)
= 25 [1 + 2 sin x.cos x + 1 – 2 sinx.cos x]
= 25 [1 + 1]
= 50
Therefore, m2 + n2 = 50
34. Evaluate the expression:
cot (12) x cot (78) x cot(13) x cot(77)
A. 11
B. 1
C. 5
D. 12
E. None of these
Correct Ans:1
Given expression is: cot (12) x cot (78) x cot(13) x cot(77)
Where, cot (12) = cot (90 – 78)
Since, cot(90 – x) = tan x
=> cot (12) = tan (78)
Similarly cot (13) = cot( 90 – 77) = tan (77)
Subs cot (12) = tan (78) and
cot (13) = tan (77) in the given expression, we get
=> cot (12) x cot (78) x cot(13) x cot(77) = tan (78) x cot (78) x tan(77) x cot(77)
Since, tan x * cot x = 1
So, tan (78) x cot (78) = 1
And also tan (77) x cot(77) = 1
=> tan (78) x cot (78) x tan(77) x cot(77) = 1
Thus, cot (12) x cot (78) x cot (13) x cot (77) = 1
35. Given tan x + cot x = 2 , then evaluate the expression tan 6 (x) + cot 6 (x) = ?
A. 9
B. 2
C. 8
D. 5
E. None of these
Correct Ans:2
Given, tan x + cot x = 2
Since, cot x = 1/ tan x
=> tan x + (1/tan x) = 2
=> (tan2 x + 1) / tan x = 2
=> tan2 x + 1 = 2 tan x
=> tan2 x - 2 tan x + 1 = 0
=> (tan x - 1)2 = 0
=> (tan x - 1) = 0
=> tan x = 1
Now, tan6 (x) + cot6 (x) = tan6 (x) + (1/tan6 x)
= (tan x)6 + (1/tan x)6
On substituting tan x = 1 in the above expression, we get
= (1)6 + (1/1)6
= 1 + 1
=> ta^6 (x) + cot6 (x) = 2
36. Find the maximum value of the expression 21 sin x + 220 cos x
A. 231
B. 223
C. 228
D. 221
E. None of these
Correct Ans: 221
Maximum value of A sin x + B cos x = sqrt(A2 + B2)
So, Maximum value of 21 sin x + 220 cos x = sqrt(212 + 2202)
= sqrt(441 + 48400)
= sqrt(48841)
= 221
Thus, Maximum value of 21 sin x + 220 cos x = 22
37. If sec x = 2x + 1 / 8 x, then evaluate sec x + tan x
A. 4x
B. 8x
C. 12x
D. 16x
E. None of these
Correct Ans:4x
38. Evaluate the expression tan (24) x tan (66) x tan(35) x tan(55)
A. 4
B. 8
C. 1
D. 11
E. None of these
Correct Ans:1
39. Find the value of tan x , if sec x + tanx = 19
A. (180/19)
B. (275/19)
C. (313/19)
D. (237/19)
E. None of these
Correct Ans:(180/19)
40. Find the value of sec x, if sec x + tanx = 19
A. (373/19)
B. (333/19)
C. (181/19)
D. (371/19)
E. None of these
Correct Ans:(181/19)
41. Find the maximum value of the expression 11 sin x + 60 cos x
A. 68
B. 61
C. 67
D. 64
E. None of these
Correct Ans:61
42. Find the sum of all the angles (in degrees) if the polygon has 9 sides.
A. 1268
B. 1267
C. 1260
D. 1264
E/ None of these
Correct Ans:1260
43. If tan(5x - 40) = cot(5y+20) then find the value of x + y.
A. 28
B. 29
C. 26
D.22
E. None of these
Correct Ans:22
44. Find the value of tan x, if sec x + tanx = 15
A. (202/15)
B. (187/15)
C. (73/7)
D.(112/15)
E. None of these
Correct Ans:(112/15)
45. Find the value of sec x, if sec x + tanx = 7
A. (88/7)
B. (74/7)
C. (73/7)
D. (25/7)
E. None of these
Correct Ans:(25/7)
46. Find the sum of all the angles (in degrees) if the polygon has 5 sides.
A. 546
B. 543
C. 548
D. 540
E. None of these
Correct Ans:540
47. Evaluate sin 10 sin 40 sin 70
A. 1/8
B. 1/2
C. 1/4
D. 1/16
E. None of the above
Correct Ans:1/8
48. Evaluate tan 15 x tan 45 x tan 75
A. 1
B. sqrt(2)
C. 1/2
D. 2
E. None of the above
Correct Ans:1
49. If sec x - tan x = m and sec x + tanx = 1 / n then which of the following is true
A. m=n
B. mn = 1
C. m + n =1
D. m - n = 1
E. None of the above
Correct Ans:m=n
50. If 2 cos x + 3 cos y = 5 then 3 sin (x + 90) + 10 sin y = ?
A. 2
B. -2
C. 3
D.1/2
E. None of the above
Correct Ans:3
51. Evaluate tan 11 x tan 23 x tan 79 x tan 67
A. 1
B. 1/3
C. 1/4
D. 1/10
E. None of the above
Correct Ans:1
52. Evaluate: sin(12) cos(78)+sin(78) cos (12)
A. 1
B. -1
C. sin(66)
D. cos(66)
E. None of these
Correct Ans:1
53. Evaluate the area of the triangle if a = 3, b = 4 and angle C = 30
A. 5
B. 3
C. 7
D. 4
E. None of these
Correct Ans:3
54. The angle of elevation of a bird sitting on the top of a tree of height is 10 meters is 60 degrees".Find the distance from the bottom of the tree
A. 19.3
B. 17.3
C. 16.3
D. 20.3
E. None of these
Correct Ans:17.3
55. From the top of a building 75 meter high, the angle of depression of ball lying on the ground was observed to be 60 degrees. Find the distance between the ball and the foot of the building.
A. 129.75
B. 130.75
C. 128.75
D. 132.75
E. None of these
Correct Ans:129.75
56. Evaluate the expression cos^4 x - sin^4 x , given that cos^2 x - sin^2 x = 3 / 5
A. (3 / 5)
B. (1 / 63)
C. (3 / 81)
D.(1 / 93)
E. None of these
Correct Ans:(3 / 5)
57. Evaluate: sin(13) cos(77)+sin(77) cos (13)
A. 0
B. 1
C. sin(64)
D. cos(64)
E. None of these
Correct Ans:1
58. Evaluate the expression cos^4 x - sin^4 x , given that cos^2 x - sin^2 x = 2 / 3
A. (1 / 2)
B. (4 / 71)
C. (2 / 3)
D. (2 / 102)
E. None of these
Correct Ans:(2 / 3)
59. The angle of elevation of a bird sitting on the top of a tree of height is 12 meter is 30 degree. Find the distance from the bottom of the tree
A. 6.96
B. 7.96
C. 5.96
D. 9.96
E. None of these
Correct Ans:6.96
60. The angle of elevation of a bird sitting on the top of a tree of height is 11 meters is 45 degrees".Find the distance from the bottom of the tree
A. 13
B. 12
C. 11
D. 14
E. None of these
Correct Ans:11
61. Evaluate: sin(15) cos(75)+sin(75) cos (15)
A. 1
B. -1
C. sin(60)
D. cos(60)
E. None of these
Correct Ans:1
62. Evaluate the area of the triangle if a = 6, b = 12 and angle C = 30
A. 20
B. 21
C. 18
D. 19
E. None of these
Correct Ans:18
63. The angle of elevation of a bird sitting on the top of a tree of height is 13 meters is 60 degrees".Find the distance from the bottom of the tree
A. 24.49
B. 3.49
C. 21.49
D. 22.49
E. None of these
Correct Ans:22.49
64. Evaluate the expression cos^4 x - sin^4 x , given that cos^2 x - sin^2 x = 5 / 7
A. (5 / 9)
B. (5 / 81)
C. (5 / 7)
D. (5 / 111)
E. None of these
Correct Ans:(5 / 7)
65. Given tan (x+15) + cot(x+15) = 2, then what will be the value of x = ?
A. 45
B. 25
C. cannot be determined
D. 30
E. None of the above
Correct Ans:30
66. Find the maximum value of the expression 5 sin x + 12 cos x
A. 17
B. -17
C. 13
D. -13
E. None of the above
Correct Ans:13
67. Evaluate the expression 3 sin x + 2 cos y, given that 2 cos x + 7 sin y = 9
A. 4.5
B. 5
C. 4
D. 0
E. None of the above
Correct Ans:0
68. Evaluate sin(1) x sin (2) x ... sin(180) = ?
A. 1
B. 180
C. -1
D. 0
E. None of the above
Correct Ans:0
69. Given sin (x+30) = sqrt(3) / 2 , then tan x + cot x = ?
A. 4 sqrt(3) / 3
B. 8 sqrt(3) / 3
C. 2 sqrt(3) / 3
D. 16 sqrt(3) / 3
E. None of the above
Correct Ans:4 sqrt(3) / 3
70. If sin (x + 45) = 1, then evaluate tan^4 x + cot^4 x = ?
A. 1/2
B. 4
C. 1/4
D. 2
E. None of the above
Correct Ans:2
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