CBSE Class 10 Mathematics Introduction to Trigonometry MCQs

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) 1/a

Answer :  a²

Question : The value of cosec 70° – sec 20° is _____
(a) 0
(b) 1
(c) 70°
(d) 20°

Answer : 0

Question : If 3 sec θ – 5 = 0 then cot θ = _____
(a) 5/3
(b) 4/5
(c) 3/4
(d) 3/5

Answer : 3/4

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

Answer : 0

Question : If sin (90 – θ) cos θ = 1 and θ is an acute angle then θ = ____
(a) 90°
(b) 60°
(c) 30°
(d) 0°

Answer : 0°

Question : The value of (1 + cos θ) (1 – cos θ) cosec θ = _____
(a) 0
(b) 1
(c) cos²θ
(d) sin²θ

Answer : 1

Question : If sec θ+ tan θ = x, then sec θ =
(a) x²+1/x
(b) x²+1/2x
(c) x²-1/2x
(d) x²-1/x

Answer :  x²+1/2x

Question : If sin θ – cos θ = 0, 0 ≤  θ ≤ 90° then the value of θ is _____
(a) cos θ
(b) 45°
(c) 90°
(d) sin  θ

Answer : 45°

Question :  sin θ/√1-sin² θ
(a) cot θ
(b) √sin θ
(c) sin θ/√cos θ
(d) tan θ

Answer : tan θ

Question : The length of the shadow of a man is equal to the height of man. The angle of elevation is
(a) 90°
(b) 60°
(c) 45°
(d) 30°

Answer : 45°

Question : The length of the shadow of a pole 30m high at some instant is 10 √3 m. The angle of elevation of the sun is
(a) 30°
(b) 60°
(c) 45°
(d) 90°

Answer : 60°

Question : Find the angle of depression of a boat from the bridge at a horizontal distance of 25m from the bridge, if the height of the bridge is 25m.
(a) 45°
(b) 60°
(c) 30°
(d) 15°

Answer : 45°

Question : The tops of two poles of height 10m and 18m are connected with wire. If wire makes an angle of 30° with horizontal, then length of wire is
(a) 10m
(b) 18m
(c) 12m
(d) 16m

Answer : 16m

Question : From a point 20m away from the foot of the tower, the angle of elevation of the top of the tower is 30°. The height of the tower is
(a) 20 √3 m
(b) 20/√ 3 m
(c) 40√ 3 m
(d) 40 /√3 m

Answer : 20/√ 3 m

Question : The ratio of the length of a tree and its shadow is 1 : 1/√3 The angle of elevation of the sun is
(a) 30°
(b) 45°
(c) 60°
(d) 90°

Answer : 60°

Question : A kite is flying at a height of 50√ 3 m above the level ground, attached to string inclined at 60° to the horizontal, the length of string is
(a) 100 m
(b) 50 m
(c) 150 m
(d) 75 m

Answer : 100 m

Question :  In given fig. 2 the perimeter of rectangle ABCD is
(a) 40 m
(b) 20 (√3 + 1) m
(c) 60 m
(d) 10(√3+1) m

Answer : 20 (√ 3 + 1) m

Question : A tree is broken at a height of 10 m above the ground. The broken part touches the ground and makes an angle of 30° with the horizontal. The height of the tree is
(a) 30 m
(b) 20 m
(c) 10 m
(d) 15 m

Answer : 30 m

Question : In the shadow of a tree is 1/√ 3 times the height of the tree, then find the angle of elevation of the sun.
(a) 30°
(b) 45°
(c) 60°
(d) 90°

Answer : 60°

Then the value of A and B is

a) 45°, 30° 

b) 45°, 15°

c) 60°, 30°

d) None of these

Answer: 45°, 15°

Question: If A, B, C are the interior angles of a triangle ABC, then

 equals to

a)

b)

c)

d)

Answer:

Question:  If

then the value of sin θ is :-

a)

b)

c)

d)

Answer:

Question: If the value of

, then the value of cosec θ is :- 

a)

b)

c)

d) 3

Answer:

Question: The value of tan θ= √2 – 1, then the value of the expression

  is:

a)

b)

c)

d)

Answer:

Question: The value of sec 45° is :-

a)

b) √2

c) 1

d)

Answer: √2

Question: The value of sin 30° cos 45° + cos 30° sin 45° is :-

a)

b)

c)

d)

Answer:

Question: The value of sin²θ + cos²θ is always :-

a) 1

b) 0

c) –1

d) 2

Answer: 1

Question: If cos (40° + x) = sin 30°, then the value of x is :-

a) 19° 

b) 23°

c) 22° 

d) 20°

Answer: 20°

Question: A rhombus of side 20 cm has two angles of 60° each, then the length of the diagonals is (in cm) :-

a) 20 √3 , 20

b) 20, √3  

c) 12 √3  , 12

d) 15 √3  , 15

Answer: 20 √3 , 20

Question: The values of tanθ and cotθ are equal when :-

a) θ = 30°

b) θ = 45°

c) θ = 90° 

d) θ = 0°

Answer: θ = 45°

Question:  If 

then the value of tan α is

a)

b)

c)

d)

Answer:

Question: If 

 then cos θ is equal to :-

a)

b)

c)

d)

Answer:

Question: Which one of the following is correct?

a) sec² α = 1 – tan² α 

b) sin² α = 1 + cos² α

c) tan α cot α = 1 

d) None of these

Answer: tan α cot α = 1 

Question: Which one of the following is true?

a) sin (90° – θ) = sin  θ 

b) cos (90° – θ) = cos  θ

c) sin (90° – θ) = cos  θ 

d) tan (90° + θ) = tan  θ

Answer: sin (90° – θ) = cos  θ 

Question: The value of sinB cos (90° - B) + cos B sin (90° - B) is

a) 0

b) 1

c) sinB cosB

d) 2 sin² B

Answer: 1

Question: The value of cos⁴ θ + sin⁴ θ + 2 cos² θ sin² θ, . when θ = 45° is

a) 1

b) 2

c)

d) 2 √2

Answer: 1

Question: On simplifying

two students got the following answers:

What can you say about this?

a) Both I and II are correct

b) Both are wrong

c) I is wrong, II is correct

d) I is correct, II is wrong

Answer: Both I and II are correct

Question: If

then the value of sec β + tan β is equal to

a) 2x

b)

c) 3x

d)

Answer: 2x

Question: In an acute angled ΔABC, a = 4 cm, b = 6 cm,

, then the value of angle A is

a) 30° 

b) 45°

c) 60° 

d) None of these

Answer: 30° 

Question. If tan (A – B) = 1/√3 and tan (A + B) = √3 ,0° < A + B ≤ 90°, A > B.Then the value of A and B is
(a) 45°, 30°
(b) 45°, 15
(c) 60°, 30°
(d) None of these

Answer: B

Question. If A, B, C are the interior angles of a triangle ABC, then cos (A+B/2) equals to
(a) cos C/2
(b) sec C/2
(c) cosec C/2
(d) sin C/2

Answer: D

Question. If tan θ = 12/5 , then the value of sin θ is :-
(a) 12/13
(b) 13/12
(c) 5/12
(d) 5/13

Answer: A

Question. If the value of sin θ = 3/5 , then the value of cosec θ is :-
(a) 13/5
(b) 1/5
(c) 5/3
(d) 3

Answer: C

Question. The value of tan θ = √2 – 1, then the value of the expression tanθ/1 + tan2θ is :-
(a) √2/4
(b) 1/4
(c) √2
(d) 1/√2

Answer: A

Question. The value of sec 45° is :-
(a) 1/√2
(b) √2
(c) 1
(d) √3/2

Answer: B

Question. The value of sin 30° cos 45° + cos 30° sin 45° is :-
(a) √2-√6/4
(b) √6/4
(c) √2/4
(d) √2+√6/4

Answer: D

Question. The value of sin²θ + cos²θ is always :-
(a) 1
(b) 0
(c) –1
(d) 2

Answer: A

Question. If cos (40° + x) = sin 30°, then the value of x is :-
(a) 19°
(b) 23°
(c) 22°
(d) 20°

Answer: D

Question. A rhombus of side 20 cm has two angles of 60° each, then the length of the diagonals is (in cm) :-
(a) 20 √3 , 20
(b) 20, 3
(c) 12 √3 , 12
(d) 15√3 , 15

Answer: A

Question. The values of tanθ and cotθ are equal when :-
(a) θ = 30°
(b) θ = 45°
(c) θ = 90°
(d) θ = 0°

Answer: B

Question. If cosec α = 13/12 , then the value of tan α is 
(a) 12/5
(b) 12/13
(c) 5/12
(d) 5/13

Answer: A

Question. If tan θ = x/y , then cos θ is equal to :-
(a) x/√x²+y²
(b) x/y
(c) y/√x²+y²
(d) x²+y²/x²-y²

Answer: C

Question. Which one of the following is correct?
(a) sec² α = 1 – tan² α
(b) sin² α = 1 + cos² α
(c) tan α cot α = 1
(d) none of these

Answer: C

Question. Which one of the following is true?
(a) sin (90° – θ) = sin θ
(b) cos (90° – θ) = cos θ
(c) sin (90° – θ) = cos θ
(d) tan (90° + θ) = tan θ

Answer: C

Question. The value of sinB cos (90° - B) + cos B sin (90° - B) is
(a) 0
(b) 1
(c) sinb cosB
(d) 2 sin² B

Answer: B

Question. The value of cos⁴ θ + sin⁴ θ + 2 cos² θ sin² θ, . when θ = 45° is
(a) 1
(b) 2
(c) 1/√2
(d) 2 √2

Answer: A

Question. On simplifying √1-cosθ/1+cosθ two students got the following answers:
I. cosec θ – cot θ II. 1/cosec θ+ cot θ
What can you say about this?
(a) both I and II are correct
(b) both are wrong
(c) I is wrong, II is correct
(d) I is correct, II is wrong

Answer: A

Question. If sec β = x + 1/4x , then the value of sec β + tan β is equal to 
(a) 2x
(b) x/2
(c) 3x 
(d) x/3

Answer: A

Question. In an acute angled ΔABC, a = 4 cm, b = 6 cm, sin B =3/4 , then the value of angle A is
(a) 30°
(b) 45°
(c) 60°
(d) none of these

Answer: A

Question: If tan A = 3/2, then the value of cos A is

a) 2/ √13

b) 2/13

c) 3/ √13

d) None of these

Answer: 2/ √13

Question: If sin(α +β)= 1, then cos(α - β) can be reduced to

a) sin2β

b) cos β

c) sin β

d) None of these

Answer: sin2β

Question: Given that sin α = 1/√2 and cos β = 1/√2, then the value of tan(α + β) is

a) not defined

b) 1

c) 0

d) √3

Answer: not defined

Question: If cos 9 α = sin α and 9α < 90°, then the value of tan 5α is

a) 1

b) 0

c) √3

d) 1/√3

Answer: 1

Question: If ΔABC is right-angled at C, then the value of cos(A + B) is

a) 0

b) 1

c) 2

d) None of these

Answer: 0

Question: The value of the expression sin 60⁰/ cos 30⁰

a) 1

b) 2

c) 1/2

d) √3/2

Answer: 1

Question: The value of the expression cosec (75° +Θ) -sec(15° -Θ) -tan(55° +Θ) +cot(35° -Θ) is

a) 0

b) 1

c) 3/2

d) –1

Answer: 0

Question:

a) 2

b) 1

c) 0

d) 3

Answer: 2

Question:

a) 1/2

b) 3/4

c) 1/3

d) 2/3

Answer: 1/2

Question: sin2A= 2sin A is true when A is

a) 0°

b) 30°

c) 45°

d) 60°

Answer: 0°

Question: The value of tangent of 90° is

a) not defined

b) 1

c) 0

d) √3

Answer: not defined

Question: If sin A= 5/13, the value of tan A is

a) 5/12

b) 12/13

c) 13/12

d) None of these

Answer: 5/12

Question: 9 sec² A-9 tan² A is equal to

a) 9

b) 8

c) 0

d) 1

Answer: 9

Question: (1 +tan Θ +sec Θ)(1 +cot Θ -cosecΘ) is equal to

a) 2

b) –1

c) 1

d) 0

Answer: 2

Question: If sec Θ +tan Θ = x, then tan Θ is equal to

a) X²-1/2X

b) X²-1/X

c) X²+1/2X

d) None of these

Answer: X²-1/2X

Question: cos⁴ A -sin⁴ A is equal to

a) 2cos² A -1

b) 2sin² A -1

c) 2sin² A +1

d) 2cos² A +1

Answer: 2cos² A -1

Question: If sin B = 12/13 , then cot B is

a) 5/12

b) 5/13

c) 12/5

d) 13/5

Answer: 5/12

Question: Given that cosΘ = a/b , then cosecΘ is

a)

b)

c)

d) None of these

Answer:

Question: If cos A +cos² A =1, then the value of the expression sin² A +sin⁴ A is

a) 1

b) 2

c) 1/2

d) None of these

Answer: 1

Question: If sinΘ -cosΘ = 0, then the value of (sin⁴ Θ +cos⁴ Θ) is

a) 1/2

b) 1/4

c) 3/4

d) None of these

Answer: 1/2

Question: The value of (sin 45°-cos 45°) is

a) 0

b) √2

c) 1

d) 1/√2

Answer: 0

Question: The value of sin² 39°+sin² 51° is

a) 1

b) 0

c) 2sin² 39°

d) 2cos² 51°

Answer: 1

Question: If ΔABC is right-angled at A, then sec (B +C) is

a) not defined

b) 2

c) 1

d) 0

Answer: not defined

Question: (sec A+tan A)(1 -sin A) is equal to

a) cos A

b) cosecA

c) sin A

d) sec A

Answer: cos A

CASE STUDY QUESTION 

Doing swing ball in a cricket match turns the ball and can put the batsman in danger. Our two famous bowlers Ashwin and Akash, throws the ball at an angle of A and B respectively. The relation between A and B are such that 𝑠𝑖𝑛(𝐴−𝐵)=12 and 𝑐𝑜𝑠(𝐴+𝐵)=0), 0°<𝐴+𝐵≤90° , 𝐴 >𝐵

Question : What is the measure of ∠ 𝐴 ?
(a) 30°
(b) 45°
(c) 60°
(d) 90°
Answer : C

Question : What is the measure of ∠ 𝐵?
(a) 30°
(b) 45°
(c) 60°
(d) 90°
Answer : A

Question : Now on the bases of value of A and B derived find 𝑐𝑜𝑠𝑒𝑐 (𝐴 – 𝐵)
(a) 0
(b) 2
(c) √2
(d) 2/√3
Answer : B

Question : What is the value of sec𝐵?
(a) 0
(b) 1
(c) ∝
(d) 2/√3
Answer : D

Raji a student of class10 has to made a project. She decides to make a bird house which is triangular in shape. She uses cardboard to make the bird house as shown in the figure. Considering the front side of bird house as a right-angled triangle PQR, right angled at R, answer the following questions

On the basis of above answer the following questions

Question : If ∠PQR = θ , the cos θ =
(a) 12/13
(b) 13/12
(c) 12/5
(d) 5/12
Answer : A

Question : Find the value of sec θ
(a) 12/13
(b) 13/12
(c) 12/5
(d) 5/12
Answer : B

Question : Find the value of tan𝜃/1+𝑡𝑎𝑛²θ
(a) 60/169
(b) 169/60
(c) 12/5
(d) 5/12
Answer : A

Question : The value of 𝑐𝑜𝑡²θ – 𝑐𝑜𝑠𝑒𝑐²θ
(a) 0
(b) 1
(c) 2
(d) -1
Answer : D

Question : The value of 𝑠𝑖𝑛²θ + 𝑐𝑜𝑠²θ
(a) 0
(b) 1
(c) 2
(d) -1
Answer : B

Question : In ΔOPQ, right-angled at P, OP = 7 cm and OQ – PQ = 1 cm, then the values of sin Q.
(a) 7/ 25
(b) 24/25
(c) 1
(d) none of the these

Question : If sin A = 24 /25 , then the value of cosA is
(a) 7/ 25
(b) 24 /25
(c) 1
(d) none of the these

Question : In ΔABC, right-angled at B, AB = 5 cm and ΔACB = 30° then the length of the side BC is
(a) 5 √3
(b) 2√3
(c) 10 cm
(d) none of these

Question : In ΔABC, right-angled at B, AB = 5 cm and ΔACB = 30° then the length of the side AC is
(a) 5 √3
(b) 2 √3
(c) 10 cm
(d) none of these

Question : sin 2A = 2 sin A is true when A =
(a) 0°
(b) 30°
(c) 45°
(d) 60°

Question : 9 sec² A – 9 tan² A =
(a) 1
(b) 9
(c) 8
(d) 0

Question : (1 + tanA + secA ) (1 + cotA – cosecA ) =
(a) 0
(b) 1
(c) 2
(d) –1

Question : (sec A + tan A) (1 – sin A) =
(a) sec A
(b) sin A
(c) cosec A
(d) cos A

Question : 1 + tan² A / 1 + cot² A =
(a) sec² A
(b) –1
(c) cot² A
(d) tan² A 

Question : If sin 3A = cos (A – 26°), where 3A is an acute angle, find the value of A.
(a) 29°
(b) 30° 
(c) 26° 
(d) 36°

Question : If tan 2A = cot (A – 18°), where 2A is an acute angle, find the value of A.
(a) 29° 
(b) 30° 
(c) 26° 
(d) none of these

Question : If sec 4A = cosec (A – 20°), where 4A is an acute angle, find the value of A.
(a) 22°
(b) 25° 
(c) 26° 
(d) none of these

Question : The value of tan 48° tan 23° tan 42° tan 67° is
(a) 1
(b) 9
(c) 8
(d) 0

Question : If ΔABC is right angled at C, then the value of cos(A + B) is
(a) 0
(b) 1
(c) ½
(d) n.d.

Question : If cos A = 24/25, then the value of sinA is
(a) 7/25
(b) 24/25
(c) 1
(d) none of the these.

Question : If ΔABC is right angled at B, then the value of cos(A + C) is
(a) 0
(b) 1
(c) ½
(d) n.d.

Question : If tanA = 4/3, then the value of cosA is
(a) 3/5
(b) 4/3
(c) 1
(d) none of the these

Question : IfΔABC is right angled at C, in which AB = 29 units, BC = 21 units and ΔABC = θ . Determine the values of cos²α + sin²α  is
(a) 0
(b) 1
(c) ½
(d) n.d.

Question : In a right triangle ABC, right-angled at B, if tan A = 1, then the value of 2 sin A cos A =
(a) 0
(b) 1
(c) ½
(d) n.d.

Question : Given 15 cot A = 8, then sin A =
(a) 3/5
(b) 4/3
(c) 1
(d) none of the these

1. In a triangle PQR, right-angled at Q, PR + QR = 25 cm and PQ = 5 cm, then the value of sin P is
(a) 7/25
(b) 24/25
(c) 1
(d) none of the these

2. In a triangle PQR, right-angled at Q, PQ = 3 cm and PR = 6 cm, then
(a) 0°
(b) 30°
(c) 45°
(d) 60°

Question. If sin (A – B) = 1/2 and cos(A + B) = 1/2 , then the value of A and B, respectively are
(a) 45° and 15°
(b) 30° and 15°
(c) 45° and 30°
(d) none of these

Question. If sin (A – B) = 1 and cos(A + B) = 1, then the value of A and B, respectively are
(a) 45° and 15°
(b) 30° and 15°
(c) 45° and 30°
(d) none of these

Question. If tan (A – B) = 1/√3 and tan (A + B) = √3 , then the value of A and B, respectively are
(a) 45° and 15°
(b) 30° and 15°
(c) 45° and 30°
(d) none of these

Question. If cos (A – B) = √3/2 and sin (A + B) = 1, then the value of A and B, respectively are
(a) 45° and 15°
(b) 30° and 15°
(c) 60° and 30°
(d) none of these

Question. The value of 2cos² 60⁰ + 3sin² 45⁰ - 3sin² 30⁰ + 2cos² 90⁰ is
(a) 1
(b) 5
(c) 5/4
(d) none of these

Question. sin 2A = 2 sin AcosA is true when A =
(a) 0°
(b) 30°
(c) 45°
(d) any angle

Question. sin A = cosA is true when A =
(a) 0°
(b) 30°
(c) 45°
(d) any angle

Question. If sinA = 12, then the value of 3cosA – 4cos³A is
(a) 0
(b) 1
(c) ½
(d) n.d.

Question. If 3cotA = 4, then the value of cos²A – sin²A is
(a) 3/4
(b) 7/25
(c) ½
(d) 24/25

Question. If 3tanA = 4, then the value of 3sinA + 2cos A/3sin A-2cosA is
(a) 1
(b) 7/25
(c) 3
(d) 24/25

2. Value of sec²26⁰ – cot²64⁰ is:
(a) 1
(b) –1
(c) 0
(d) 2

3. Product tan1⁰.tan2⁰.tan3^{0  _{_______}} tan89⁰ is:
(a) 1
(b) –1
(c) 0
(d) 90

8. If Sin (A + B) = 1 = cos(A – B) then
(a) A = B = 90⁰
(b) A = B = 0⁰
(c) A = B = 45⁰
(d) A = 2B

9. The value of sin60⁰cos30⁰ – cos60⁰sin30⁰ is
(a) 1
(b) –1
(c) 0
(d) none of these

10. The value of 2sin² 30⁰ -3cos² 45⁰ + tan² 60⁰ + 3sin² 90⁰ is
(a) 1
(b) 5
(c) 0
(d) none of these