CBSE Class 10 Mathematics Introduction to Trigonometry MCQs Set 06

Question. The angle of elevation of the top of two vertical towers as seen from the middle point of the line joining the feet of the towers are 60° and 30° respectively. The ratio of heights of the towers is :-
(a) 2 : 1
(b) √3 : 1
(c) 3 : 2
(d) 3 : 1

Answer: D

Question. A person standing on the bank of a river observes that the angle of elevation of the top of a tree on the opposite bank of the river is 60° and when he retires 40 m away from the tree, the angle of elevation becomes 30°. The breadth of the river is
(a) 40 m
(b) 20 m
(c) 30
(d) 60 m

Answer: B

Question. The top of a hill observed from the top and bottom of a building of height h is at angles of elevation p and q respectively. The height of hill is :-
(a) hcotp/ cotq − cotp
(b) hcotp /cotp−cotq
(c) htanp/ tanp−tanq 
(d) htanp/ tanq − tanp 

Answer: D

Question. 1- tan² 45°/1 + tan² 45°
(a) sin 45°
(b) 0
(c) cos 45°
(d) tan 45°

Answer: B

Question. The value of tan 15° tan 20° tan 70° tan 75° is
(a) 2
(b) 0
(c) 1
(d) -1

Answer: C

Question. If cotθ = 7/8 , then the value of (1+sinθ)/(1-sinθ)/1+cosθ)(1-cosθ) is
(a) 64/49
(b) 7/8
(c) 8/7
(d) 49/64

Answer: D

Question. If sin α =1/√2 and tan β = 1, then the value of cos (α+β) is
(a) 3
(b) 1
(c) 2
(d) 0

Answer: D

Question. Evaluate: 4 sin² 60° + 3 tan² 30° – 8 sin 45° cos 45°
(a) 0
(b) 1
(c) 2
(d) 5

Answer: A

Question. The value of (sin²θ +1/1 +tan² θ) =
(a) 0
(b) 1
(c) 2
(d) 5

Answer: B

Question. The value of x such that ² cosec² 30° + x sin² 60° – 3/ 4 tan² 30° = 10, is
(a) 1
(b) 2
(c) 3
(d) 5

Answer: C

Question. If tan A = 5/12 , then (sin A + cos A) ⋅ sec A is equal to
(a) 11/ 12 
(b) 13/ 12
(c) 12 /19
(d) 17 /12

Answer: D

Question. If 4 tan θ = 3, then the value of 4 sin θ − cos θ /4 sin θ + cos θ is
(a) 1/ 2
(b) 1/ 3
(c) 1/ 4 
(d) 1/ 5

Answer: A

Question. If tan A = n tan B and sin A = m sin B, then cos² A =
(a) m^2 − 1/n² − 1
(b) m² + 1/n² + 1
(c) 1 − m²/1 + m²
(d) 1+ m² /1 − m²

Answer: A

Question. A balloon of radius r subtends an angle a at the eye of an observer and the elevation of the centre of the balloon from the eye is b, the height h of the centre of the balloon is given by :-
(a) r sinβ/ sin α
(b) r sin β sin α
(c) r sinβ/ sin( α/2)
(d) r sinα/ sin(β/2) 

Answer: C

Question. A man observes that when he moves up a distance c metres on a slope, the angle of depression of a point on the horizontal plane from the base of the slope is 30°, and when he moves up further a distance c metres, the angle of depression of that point is 45°. The angle of inclination of the slope with the horizontal is :-
(a) 60°
(b) 45°
(c) 75°
(d) 30°

Answer: C

Question. Which of the following statement is true:
(a) cosec A/sin A = cos A
(b) cos A/sin A =sec A
(c) sin A/cosec A = cot A
(d) sin A/cos A = tan A 

Answer: D

Question. If x cos A = 1 and tan A = y, then the value of x²-y² is
(a) -1
(b) 0
(c) 1
(d) 2

Answer: C

Question. If 2sin²θ =√3, then the value of θ
(a) 60°
(b) 45°
(c) 0°
(d) 30°

Answer: D

Question. Choose the correct option. Justify your choice.(sec A + tan A) (1 – sin A)
(a) cos A
(b) sec A
(c) sin A
(d) cosec A

Answer: A

Question. If triangle ABC is right angled at C, then the value of sec (A + B) is
(a) 0 
(b) 1
(c) 2/√3
(d) not defined

Answer: D

Question. Evaluate: sin30° + tan 45° - cosec 60°/sec 30° + cos60° + cot 45°
(a) 3 √3 + 2/3√3 -2
(b) 3 √3/−4/ 3√3 +4
(c) 3√3/ + 3 √3 − 9 
(d) None of these

Answer: B

Question. The value of (sin⁴θ – cos⁴θ + 1) cosec²θ is
(a) 0
(b) 1
(c) 2
(d) 5

Answer: C

Question. Given that sin a = √3/ 2 and cos b = 0, then the value of β – α is
(a) 0°
(b) 90°
(c) 60°
(d) 30°

Answer: D

Question. If 7 sin²θ+ 3 cos²θ = 4, then tan θ =
(a) ± 1/3
(b) ± 1/ 2
(c) ± 1 /√3
(d) ± 1 /√2

Answer: C

Question. A man standing on a level plane observes the elevation of the top of a pole to be a. He then walks a distance equal to double the height of the pole and finds that the elevation is now 2a. Then a =
(a) π/6
(b) π/4
(c) π/12
(d) π/8

Answer: C

Question. If A and B are acute angles and sin A = cos B, then the value of (A + B) is
(a) 0°
(b) 90°
(c) 30°
(d) 60°

Answer: B

Question. If sinθ =5/13 then cosθ =
(a) 13/12
(b) √5/13
(c) 12/5
(d) 12/13

Answer: D

Question. If sin θ = cos θ, then find the value of 2 tan θ + cos² θ.
(a) 2 /3
(b) 3 /4
(c) 5 /2
(d) 0 

Answer: C

Question. If sin θ + cos θ = √2 cos θ, (θ ≠ 90°) then the value of tan θ is
(a) √2 −1
(b) √2 +1
(c) √2
(d) − √2

Answer: A

Question. The angle of elevation of a cloud at a height h above the level of water in a lake is a and the angle of depression of its image in the lake is b. The height of the cloud above the surface of the lake is equal to
(a) h(tanβ + tanα)/ (tanβ − tanα) 
(b) hcos(α+β)/ sin(β−α) 
(c) h(cotα + cotβ)/ cosα −cosβ
(d) h

Answer: A

Question. The value of tan 1° tan 2° tan 3° ... tan 89° is
(a) 0
(b) 1
(c) − 1
(d) 2

Answer: B

Question. If sin A + sin² A=1 , then the value of cos² A + cos² A is
(a) – 1
(b) 2
(c) 0
(d) 1

Answer: D

Question. The value of cos 48° - sin 42° is
(a) 0
(b) 1
(c) √2
(d) 1/2

Answer: A

Question. The value of (sin 30° + cos 60°)
(a) 1
(b) 2
(c) 0
(d) None of these

Answer: A

Question. A pole of 6 m high casts a shadow 2 √3 m long, then sun’s elevation is
(a) 60°
(b) 45°
(c) 30°
(d) 90°

Answer: A

Question. The value of tan 30°/cot 60° is
(a) 1
(b) 1/√3
(c) 1/√2
(d) √2

Answer: A

Question. sin² A + sin² A tan² A =
(a) tan² A
(b) cos² A
(c) None of these
(d) sin² A

Answer: A

Question. If cot θ + cos θ = p and cot θ − cos θ = q, then the value of p² − q² is :
(a) 2√ pq
(b) 4 √pq
(c) 2pq
(d) 4pq

Answer: B

Question. If tan A + sin A = m and tan A − sin A = n, then (m² −n²)²/mn =
(a) 4
(b) 3
(c) 16
(d) 9

Answer: C

Question. The value of 2tan² 45° +cos² 30° - sin² 60° is
(a) 0
(b) 1
(c) 2
(d) -2

Answer: C

Question. Choose the correct option and justify your choice:sin 2A = 2 sin A is true when A =
(a) 45°
(b) 0°
(c) 30°
(d) 60

Answer: B

Question. 2 tan² 45° + cos² 30° – sin² 60° equals
(a) 1
(b) 2
(c) 5
(d) 6

Answer: B

Question. At some time of the day, the length of the shadow of a tower is equal to height. Then the sun’s altitude at that time is
(a) 30°
(b) 60°
(c) 90°
(d) 45°

Answer: D

One Word Questions :

Question. If sin θ = 3/5 , then find the value of 5cosθ ×sinθ .
Answer: 12/5

Question. If tanθ = 12/5 then find the value of 13 sinθ/3 .
Answer: 4

Question. If cos θ = 3/2 , then find the value of 8sec²θ + tan2θ + 1 .
Answer: 4

Question. If 1+ 2sin²θ cos²θ = sin²θ + cos²θ + 4k sin²θ cos²θ , then find the value of k.
Answer: 1/2

Question. If cos² 20°/2(sin² 59° sin2 31°) 2/k , then find the value of k.
Answer: 4

Question. If cosec² θ = 3/2 , then find the value of 2(cosec²θ + cot²θ ) .
Answer: 4

Question. If sin θ = 1/3 , then find the value of 2cosec²θ + cot2θ + 1 .
Answer: 27

Question. Find the value of tan 50 × tan 300 × 4 tan 85⁰
Answer: 4/√3

Question. If tanθ = 4, then find the value of 1/10 (tan² θ + 2sec² )
Answer: 5

Question. If tanθ tan 45⁰ = 1, then find the value of θ
Answer: 45°

Question. In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:
(a) If both Assertion and Reason are correct and Reason is the correct explanation of Assertion.
(b) If both Assertion and Reason are correct, but Reason is not the correct explanation of Assertion.
(c) If Assertion is correct but Reason is incorrect.
(d) If Assertion is incorrect but Reason is correct.

Question. Assertion: In a right angled triangle, if tan θ = 3/ 4 , the greatest side of the triangle is 5 units.
Reason: (greatest side)² = (hypotenuse)² = (perpendicular)² + (base)².

Answer: A

Question. Assertion : In a right angled triangle, if cos θ = 1/ 2 and sin θ = √3/ 2 , then tan θ = √3
Reason: tan θ = sinθ/ cos θ 

Answer: A