CBSE Class 10 Introduction to Trigonometry Sure Shot Questions Set 02

Question. If tan A = 4/3 , the value of sin A is
(a) 4/5
(b) 3/4
(c) 5/3
(d) 7/5
Answer : A

Question. If 3 tan A = 4, then the value of  3 sin A + cos A / 3 sin A - 2 cos A is:
(a) 4
(b) 11/15
(c) 7/15
(d) 3
Answer : D

Question. If sin θ + cos θ = cos θ, (θ􀀀􀉲 90°) then the value of tan θ is:
(a) √2 - 1
(b) √2 + 1
(c) √2
(d) – √2
Answer : A

Question. Given that sin a = √3 / 2 and cos B = 0, then the value of B - a is:
(a) 0°
(b) 90°
(c) 60°
(d) 30°
Answer : D

Question. If sin (A + B) = cos (A - H) = 1, then
(a) A = B = 0
(b) A = B = 45°
(c) A = 60°, B = 30°
(d) None of these
Answer : B

Question. If cos A = 5/13 , find the value of tan A + cot A
(a) 169/60
(b) 12/13
(c) 1
(d) 60/169
Answer : A

Question. If 5x = sec θ and 5/x = tan θ then find the value of (x² - 1/x²)
(a) 5
(b) 1/5
(c) 2/5
(d) 0
Answer : B

Question. If sin A + sin² A = 1, then the value of the expression (cos² A + cos⁴ A) is:
(a) 1
(b) 1/2
(c) 2
(d) 3 
Answer : A

Question. The value of (1 + cos θ) (1 - cos θ) cosec² θ =
(a) 0
(b) 1
(c) cos² θ
(d) sin² θ
Answer : B

Question. If sin θ – cos θ = 0, then the value of (sin⁴ θ + cos⁴ θ) is:
(a) 1
(b) 3/4
(c) 1/2
(d) 1/4]
Answer : C

Question. If θ = 45° then sec θ cot θ – cosec θ tan θ is
(a) 0
(b) 1
(c) 2
(d) 3
Answer : A

Question. If x = a sin θ and y = a cos θ, then the value of x² + y² is
(a) a
(b) a²
(c) 1
(d) b²
Answer : B

Question. 4 tan² A – 4 sec² A is equal to:
(a) 2
(b) 3
(c) 4
(d) –4
Answer : D

Question. If 3 cos θ = 1, then cosec θ is equal to:
(a) 2√2
(b) 3/2√2
(c) 2√3/3
(d) 4/3√2
Answer : B

Question. If cosec θ – cot θ = 1/3, then the value of cosec θ + cot θ is:
(a) 1
(b) 2
(c) 3
(d) 4
Answer : C

Question. If 2 sin 2θ = 3 , then the value of θ is:
(a) 90°
(b) 30°
(c) 60°
(d) 45°
Answer : B

Question. If the height and length of the shadow of a man are the same, then the angle of elevation of the sun is:
(a) 45°
(b) 60°
(c) 90°
(d) 120°
Answer : A

Question. If a man standing on a platform 3 metres above the surface of a lake observes a cloud and its reflection in the lake, then the angle of elevation of the cloud is equal to the angle of depression of its reflection. 
Answer : False.

Question. cos θ = a² + b² / 2ab, where a and b are two distinctbnumbers such that ab > 0. 
Answer : False.

Question. The angle of elevation of the top of a tower is 30°. If the height of the tower is doubled, then the angle of elevation of its top will also be doubled.
Answer : False.

Question. If the height of a tower and the distance of the point of observation from its foot, both, are increased by 10%, then the angle of elevation of its top remains unchanged.
Answer : True.

Fill in the Blanks

Fill in the blanks/tables with suitable information:

Question. Simplest form of 1 + cot2 A / 1 + tan² A is .................... .
Answer : (tan²A)

Question. If tan A = 1, then 2 sin A cos A = ....................
Answer : 1

Question. The value of (sin² θ + 1 / 1 + tan² θ) ....................
Answer : 1

Question. Simplest form of (1 - cos² A) (1 + cot²A) is .................... . 
Answer : 1

Question. If 3 sec θ - 5 = 0 then cot θ = .................... .
Answer : 3/4

Question. If sin θ – cos θ = 0, 0 ≤ θ ≤ 90° then the value of q is .................... .
Answer : 45º

Question. cos 1° cos 2° cos 3° ......... cos 180° = .................... .
Answer : 0

Question. If tan θ = √3 , then sec θ = ................... .
Answer : tan θ = √3 gives θ = 60°
So, sec θ = sec 60° = 2

Question. Maximum value of 1/cosecθ is .................... .
Answer : 1/cosec θ = 1/1 = sin θ
As, sin θ ≤ 1, 1/cosec θ ≤ 1
Thus, maximum value of 1/cosec θ is 1.

Question. If tan θ + cot θ = 2, then the value of tan² θ + cot² θ is .................... .
Answer : tan² θ + cot² θ = (tan θ + cot θ)² – 2 tan θ cot θ
= (2)² – 2 × 1
= 2

Please click the link below to download CBSE Class 10 Introduction to Trigonometry Sure Shot Questions Set B.