# Trigonometry Questions

Solve the given easily to difficult level problems using Trigonometry. Trigonometry Questions with Answers are provided here, so that individuals can prepare well for this topic and score good marks in the examination. These 55+ Trigonometry Problems with solutions will helps you at the time of practice.

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Candidates can match out their selected option with the answers that are provided at the end of this page. Explanation of important and selected Trigonometry Questions is also provided here, so that individuals can go through these questions before solving out the practice questions.

## Trigonometry Questions

Trigonometry Questions with Solutions

Question 1) If cos 11π/6 = x, then the value of x is:

(a) -√3/2

(b) 1/2

(c) 2

(d) √3/2

Explanation:

According to the given information,

x = cos 11π/6

⇒ x = cos (2π – π/6)

⇒ x = cos(π/6)

∴ x = √3/2

Question 2) If tan 45° + cosec 30° = x, then find the value of x.

(a) √3

(b) (1 – 2√2)/√2

(c) (√3 – 4)/2√3

(d) 3

Explanation:

We know that,

tan 45° = 1

cosec 30° = 2

According to the given information,

x = tan 45° + cosec 30° = 1 + 2 = 3

Get Here: Trigonometry Formulas & Identities

Question 3) The value of cos225° + cos270° is

(a) -√2

(b) 2

(c) -1/√2

(d) 1

Explanation:

From the given data

⇒ cos(180 + 45)° + cos (270)° = – cos(45°) + 0 = – 1/√2

Question 4) If cot 60° + cosec 60° = x, then the value of x is

(a) (1 – 2√2)/√2

(b) (√3 – 4)/2√3

(c) 1

(d) √3

Explanation:

cot 60° + cosec 60° = x

(1/√3) + (2/√3) = x

3/√3 = x

x = √3

∴ x = √3

Question 5) What is the value of [sin(90° – A) + cos(180° – 2A)] / [cos(90° – 2A) + sin(180° – A)]?

(a) sin(A/2).cosA

(b) cot(A/2)

(c) tan(A/2)

(d) sinA.cos(A/2)

Explanation:

⇒ [sin(90° – A) + cos(180° – 2A)] / [cos(90° – 2A) + sin(180° – A)]

⇒ (cosA – cos2A) / (sin2A + sinA)

⇒ [2sin{(A + 2A)/2}.sin{(2A – A)/2}] / [2sin{(A + 2A)/2}.cos{(2A – A)/2}]

⇒ [(sin 3A/2) / (sin 3A/2)] × [(sin A/2) / (cos A/2)]

⇒ tan(A/2)

Question 6) If cot(A/2) = x, then the value of x is?

(a) √[(1 + cosA)/(1 – cosA)]

(b) cosecA – cotA

(c) √[(1 – cosA)/2]

(d) √[(1 + cosA)/2]

Answer 6) (a) √[(1 + cosA)/(1 – cosA)]

Explanation:

As per the given data,

cot (A/2) = x

cos (A/2)/sin (A/2) = x

we know that:

cos2A = (1 + cos 2A)/2

sin2A = (1 – cos 2A)/2

√(1+cosA2)√(1−cosA2)√(1+cosA2)√(1−cosA2) = x

x = √(1+cosA)√(1−cosA)

Also Check Out: Trigonometry Short Tricks

Question 7) What is the value of [1 – tan(90° – θ) + sec(90° – θ)]/[tan(90° – θ) + sec(90° – θ) + 1]?

(a) cot(θ/2)

(b) tan(θ/2)

(c) sin θ

(d) cos θ

Explanation:

⇒ [1 – tan(90° – θ) + sec(90° – θ)]/[tan(90° – θ) + sec(90° – θ) + 1]

Let the value θ = 30°
⇒ [1 – tan60° + sec60°]/[tan60° + sec60° + 1]

⇒ (1 – √3 + 2)/(1 + √3 + 2)

⇒ {√3(√3 – 1)}/{√3(√3 + 1)}

Rationalizing,

⇒ (√3 – 1)/(√3 + 1) × (√3 – 1)/(√3 – 1)

⇒ (√3 – 1)2/{(√3)2 – 12}

⇒ 2 – √3

⇒ tan15° = tan(30°/2) = tan(θ/2)

Question 8) The value of sin 10° sin 30° sin50° sin 70° will be –

(a) 4/25

(b) 1/16

(c) 1/8

(d) 3/16

Explanation:

sin 10° sin 30° sin 50° sin 70° = (1/2) sin10° sin50° sin70°

Multiplying and dividing by 2cos10° we get,

∴ sin 10° sin 30° sin50° sin 70° = (1/2) × 2 × cos10° sin10° sin50° sin70° × (1/(2cos10°))

= sin20° sin50° sin70° × (1/(4cos10°))      —-(∵ sin2A = 2sinAcosA)

Multiply and divide by 2,

sin 10° sin 30° sin50° sin 70° = 2sin20° sin50° sin70° × (1/8cos10°)

= 2sin20° sin50° sin(90 – 20)° × (1/8cos10°)

= 2sin20° sin50° cos20° × (1/8cos10°)

= Sin40° sin50° × (1/8cos10°)      —-(∵ sin2A = 2sinAcosA)

Multiply and divide by 2,

= 2 × Sin40° sin(90 – 40)° × (1/16cos10°)

= 2 × Sin40° cos40° × (1/16cos(90 – 80)°)

= sin80°/(16sin80°) = (1/16)

∴ sin 10° sin 30° sin50° sin 70° = 1/16

Question 9) If tan θ + sec θ = (x – 2)/(x + 2), then what is the value of cos θ?

(a) (x2 – 1)/(x2 + 1)

(b) (2x2 – 4)/(2x2 + 4)

(c) (x2 – 4)/(x2 + 4)

(d) (x2 – 2)/(x2 + 2)

Answer 9) (c)  (x2 – 4)/(x2 + 4)

Explanation:

If tanθ + secθ = (x – 2)/(x + 2)       —-(1)

Then, secθ – tanθ = (x + 2)/(x – 2)        —-(2)

By adding equation (1) and (2)

2secθ = (x + 2)/(x – 2) + (x – 2)/(x + 2)

⇒ 2secθ = {(x – 2)2 + (x + 2)2}/(x2 – 4)

⇒ 2secθ = {2(x2 + 4)}/(x2 – 4)

∴ cosθ = (x– 4)/(x2 + 4)

Get Here: 21+ Geometry Practice Questions

Question 10) Two supplementary angles are in the ratio 3:2. The angles are

(a) 114°, 66°

(b) 108°, 72°

(c) 54°, 36°

(d) 33°, 57°

Explanation:

By definition the sum of two supplementary angles = 180°

The two supplementary angles are in the ratio 3:2

∴ The two angles can be given by 3x & 2x

So, we can say 3x + 2x = 180 [As, the sum of two supplementary angles = 180°]

⇒ x = 36°

∴ The two angles are:

3 × 36° = 108° & 2 × 36° = 72°

Trigonometry Practice Questions

Answers for these questions are available at the end.

Question 1) What is the value of [2cot(π  – A) /2] / [1 + tan2(2π  – A) /2]?

1. 2sin2A/2
2. cosA
3. sinA
4. 2cos2A/2

Question 2) If f(x) = sin2x + cosec2 x, then the minimum value of f(x) is ________.

1. 1
2. 5
3. 2
4. 3

Question 3) What is the simplified value of sin2A/(1 + cos2A)?

1. tanA
2. cotA
3. sinA
4. cosA

Question 4) If sinA + sin2A = 1 then what is the value of cos2A + cos4A?

1. ½
2. 1
3. 2
4. 3

Question 5) What is the value of [(tan5θ + tan3θ)/4cos4θ (tan5θ – tan3θ)]?

1. sin2θ
2. cos2θ
3. tan4θ
4. cot2θ

Question 6) If cosπ/2x=x2−2x+2, the value of x will be:

1. 0
2. 1
3. -1
4. None of the above

Question 7) What is the value of sin (90° + 2A)[4 – cos2(90° – 2A)]?

1. 2(cos3A – sin3A)
2. 2(cos3A + sin3A)
3. 4(cos6A + sin6A)
4. 4(cos6A – sin6A)

Question 8) Which one of the following is true for 0° < θ < 90°, θ ≠ 0°, 90° ?

1. cosθ > cos2θ
2. cosθ < cos2θ
3. cosθ ≥ cos2θ
4. cosθ ≤ cos2θ

Question 9) What is the value of [(cos7A + cos5A) / (sin7A – sin 5A)]?

1. tan A
2. tan 4A
3. cot 4A
4. cot A

Question 10) From a point, 40 m apart from the foot of a tower, the angle of elevation of its top is 60°. The height of the tower is

1. 120√3 cm
2. 40/√3 cm
3. 40√3 m
4. 40√2 m

Question 11) What is the value of tan 6° tan 36° tan 84° tan 54° tan 45°?

1. 1/2
2. 1/√2
3. 1
4. 1/3

Question 12) A tree is 70 meters high. Its shadow is x metres shorter when the sun’s altitude is 45° than when it is 30°. The value of x in metres is

1. 70√3
2. 70(√3 – 1)
3. 70(√3 + 1)
4. 70

Question 13) If (cotA – tan A)/2 = x, then the value of x is

1. tan2A
2. cot2A
3. tanA
4. cotA

Question 14) What is the simplified value of sec6 A – tan6 A – 3 sec2 A tan2 A?

1. -1
2. 0
3. 1
4. sec A tan A

Question 15) If θ be acute angle and cosθ = 15/17, then the value of cot (90° – θ) is

1. 2√8/15
2. 8/15
3. √2/7
4. 8√7/17

Question 16) If cotα = 3, then the value of (sin3α + cos3α)/cosα is ?

1. 25/27
2. 14/15
3. 9
4. 11/15

Solve Here: Chain Rule Aptitude Questions and Answers

Question 17) The angles of elevation of the top of a building from the top and bottom of a tree are x and y respectively. If the height of the tree is h metre, then, in metre, the height of the building is.

1. h cotx/(cotx – coty)
2. h coty/(cotx + coty)
3. h cotx/(cotx + coty)
4. h coty/(cotx – coty)

Question 18) If xsin3θ + ycos3θ = sinθ cosθ and x sinθ – y cosθ = 0, then the value of x2 + y2 equals

1. 1
2. 1/2
3. 3/2
4. 2

Question 19) A boy standing in the middle of a field, observes a flying bird in the north at an angle of elevation of 30° and after 2 minutes, he observes the same bird in the south at an angle of elevation of 60°. If the bird flies all along in a straight line at a height of m, then its speed in km/h is

1. 5
2. 3
3. 9
4. 6

Question 20) If sin(x + y)/sin(x – y) = (a + b)/(a – b), then the value of tanx/tany is

1. a/b
2. b/a
3. ab
4. (a – b)/(a + b)

Question 21) Two persons are on either side of a temple, 75 m high, observe the angle of elevation of the top of the temple to be 30Â° and 60Â° respectively. The distance between the persons is

1. 2 m
2. 100 m
3. 7 m
4. 2 m

Question 22) 2 – cos2θ = 3sinθcosθ, sinθ ≠ cosθ then tanθ is

1. 1/2
2. 0
3. 2/3
4. 1/3

Question 23) A person 1.8m tall is 20√3 away from a tower. The angle of elevation from his eye to the top of the tower is 30°. Find height of the tower is?

1. 8m
2. 8m
3. 6m
4. 8m

Question 24) Ram and Shyam are 10 km apart. They both see a hot air balloon passing in the sky making an angle of 60° and 30° respectively. What is the height at which the balloon could be flying?

1. (5√3)/2
2. 5√3
3. Both a and b
4. √3

Question 25) If cos θ + sec θ = 2, the value of cos6 θ + sec6 θ is

1. 4
2. 8
3. 1
4. 2

Question 26) If 0°<θ<90°
2sinÂ²θ + 3cosθ = 3, then the value of θ is ?

1. 30°
2. 60°
3. 45°
4. 75°

Get Here: Permutation Combination Questions

Question 27) What is the value of (2 + tan 60º) ?

1. 3
2. 2/√3
3. 4/√3
4. 2 + √3

Question 28) What is the value of (1/√3) + cos 60º

1. (2 + 2√3)/√3
2. (2 + √3)/2√3
3. 7/3
4. (√2 + 1)/√2

Question 29) If sinθ = 8/17, then secθ is equal to

1. 15/17
2. 17/15
3. 18/15
4. 15/18

Question 30) sin2 20° + sin2 70° – tan2 45° = ?

1. 2
2. 0
3. 1
4. 1/2

Question 31) From the top of a building 30 meter high, the angle of depression of ball lying on the ground was observed to be 30 degree. Find the distance between the ball and foot of the building.

1. 4
2. 4
3. 4
4. 4

Check Out: 22+ Partnership Questions and Answers

Question 32) Evaluate: sin(18) cos(72)+sin(72) cos (18)

1. 0
2. -1
3. 1
4. cos(54)

Question 33) Evaluate: sin(21) cos(69)+sin(69) cos (21)

1. 1
2. -1
3. sin(48)
4. cos(48)

Question 34) From the top of a building 40 meter high, the angle of depression of ball lying on the ground was observed to be 60 degree. Find the distance between the ball and foot of the building.

1. 2
2. 2
3. 2
4. 2

Question 35) Evaluate the area of the triangle if a = 7, b = 12 and angle C = 90.

1. 44
2. 45
3. 46
4. 42

Question 36) Evaluate: sin(17) cos(73)+sin(73) cos (17)

1. 0
2. 1
3. sin(56)
4. cos(56)

Question 37) Evaluate: sin(20) cos(70)+sin(70) cos (20)

1. 0
2. –1
3. 1
4. cos(50)

Question 38) The angle of elevation of a bird sitting on the top of a tree of height is 28 meter is 45 degree.Find the distance from the bottom of the tree

1. 26
2. 27
3. 28
4. 29

Question 39) From the top of a building 20 meter high, the angle of depression of ball lying on the ground was observed to be 45 degree. Find the distance between the ball and foot of the building.

1. 22
2. 20
3. 19
4. 23

Question 40) Evaluate the area of the triangle if a = 7, b = 36 and angle C = 90.

1. 125
2. 122
3. 124
4. 126

Question 41) The angle of elevation of a bird sitting on the top of a tree of height is 37meter is 45 degree”.Find the distance from the bottom of the tree

1. 36
2. 37
3. 39
4. 74

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Question 42) Evaluate the area of the triangle if a = 14, b = 12 and angle C = 30

1. 41
2. 44
3. 43
4. 42

Question 43) Evaluate: sin(16) cos(74)+sin(74) cos (16)

1. 1
2. -1
3. sin(58)
4. cos(58)

Question 44) Evaluate the area of the triangle if a = 6, b = 12 and angle C = 30

1. 20
2. 21
3. 18
4. 19

Question 45) Evaluate: sin(15) cos(75)+sin(75) cos (15)

1. 1
2. -1
3. sin(60)
4. cos(60)

Check Here: Discount Questions and Answers

Question 46) 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

1. 96
2. 96
3. 96
4. 96

Question 47) Evaluate the area of the triangle if a = 4, b = 8 and angle C = 60

1. 92
2. 92
3. 92
4. 92

Question 48) Evaluate: sin(13) cos(77)+sin(77) cos (13)

1. 0
2. 1
3. sin(64)
4. cos(64)

Question 49) Evaluate tan 11 x tan 23 x tan 79 x tan 67

1. 1
2. 1/3
3. 1/4
4. 1/10

Get Here: Percentage Aptitude Questions

Question 50) If 2 cos x + 3 cos y =  5 then 3 sin (x + 90) + 10 sin y = ?

1. 2
2. -2
3. 3
4. 1/2