Ncert Exemplar Trigonometry

Question 1

If sinθ  + cosecθ = 2, then sin²θ + cosec²θ is equal to

Accepted Answer

2

Answer

1

Answer

4

Answer

None of these

Question 2

If f(x) = cos² x + sec² x, then

Accepted Answer

f(x) ≥ 2

Answer

f(x) < 1

Answer

f(x) = 1

Answer

2 < f(x) < 1

Question 3

If tanθ
 = 1/2 , and tanx
 = 1/3, then the value of θ
 + x
 is

Accepted Answer

π/4

Answer

π/6

Answer

π

Answer

0

Question 4

Which of the following is not correct?

Accepted Answer

sec θ = 1/2

Answer

sin θ = -1/5

Answer

cos θ = 1

Answer

tan θ = 20

Question 5

The value of tan 1° tan 2° tan 3° ... tan 89° is

Accepted Answer

1

Answer

0

Answer

1/2

Answer

Not defined

Question 6

The value of $(1 – tan² 15°) / (1 + tan² 15°)$ is

Accepted Answer

√3/2

Answer

1

Answer

√3

Answer

2

Question 7

The value of cos 1º cos 2º cos 3° ... cos 179° is

Accepted Answer

0

Answer

1/√2

Answer

1

Answer

-1

Question 8

If tan θ = 3 and θ lies in third quadrant, then the value of sin θ is

Accepted Answer

-3/√10

Answer

1/√10

Answer

-1/√10

Answer

3/√10

Question 9

The value of tan 75° – cot 75° is equal to

Accepted Answer

2√3

Answer

2+√3

Answer

2-√3

Answer

1

Question 10

Which of the following is correct?

Accepted Answer

sin 1°< sin 1

Answer

sin1°> sin 1

Answer

sin 1° = sin 1

Answer

sin 1° = (π/180) sin 1

Question 11

If $tan α = m/(m+1)$ , $tan β = 1/(2m+1)$ , then α + β is equal to

Accepted Answer

π/4

Answer

π/2

Answer

π/3

Answer

π/6

Question 12

The minimum value of 3 cosx + 4 sinx + 8 is

Accepted Answer

3

Answer

5

Answer

9

Answer

7

Question 13

The value of tan 3A – tan 2A – tan A is equal to

Accepted Answer

tan 3A tan 2A tan A

Answer

– tan 3A tan 2A tan A

Answer

tan A tan 2A – tan 2A tan 3A – tan 3A tan A

Answer

None of these

Question 14

The value of sin (45° + θ) − cos (45° – θ) is

Accepted Answer

0

Answer

2 cosθ

Answer

2 sinθ

Answer

1

Question 15

The value of cot (π/4 + θ) cot (π/4 – θ) is

Accepted Answer

1

Answer

-1

Answer

0

Answer

Not defined

Question 16

cos 2θ cos 2φ + sin² (θ – φ) – sin² (θ + φ) is equal to

Accepted Answer

cos 2(θ + φ)

Answer

sin 2(θ + φ)

Answer

sin 2(θ – φ)

Answer

cos 2(θ – φ)

Question 17

The value of cos 12° + cos 84° + cos 156° + cos 132° is

Accepted Answer

-1/2

Answer

1/2

Answer

1

Answer

-1/8

Question 18

If tan A = 1/2, tan B = 1/3, then tan (2A + B) is equal to

Accepted Answer

3

Answer

1

Answer

2

Answer

4

Question 19

The value of sin (π/10) sin (13π/10) is

Accepted Answer

-1/4

Answer

1/2

Answer

-1/2

Answer

1

Question 20

The value of sin 50° – sin 70° + sin 10° is equal to

Accepted Answer

(√5-1)/8

Answer

(√5+1)/8

Answer

(√5+1)/5

Answer

(√5+1)/(2√2)

Question 21

If sin θ + cos θ = 1, then the value of sin 2θ is equal to

Accepted Answer

0

Answer

1

Answer

1/2

Answer

-1

Question 22

If α + β = π/4, then the value of (1 + tan α) (1 + tan β) is

Accepted Answer

2

Answer

1

Answer

-2

Answer

Not defined

Question 23

If sin θ = -4/5 and θ lies in third quadrant then the value of cos (θ/2) is

Accepted Answer

-1/√5

Answer

1/5

Answer

-1/√10

Answer

1/√10

Question 24

Number of solutions of the equation tan x + sec x = 2 cos x lying in the interval [0, 2π] is

Accepted Answer

2

Answer

0

Answer

1

Answer

3

Question 25

The value of sin (π/18) + sin (π/9) + sin (π/6) + sin (π/9) is given by

Accepted Answer

sin (7π/18) + sin (4π/9)

Answer

sin (7π/18) + sin (π/9)

Answer

cos (π/6) + cos (3π/7)

Answer

cos (π/9) + sin (π/9)

Question 26

If A lies in the second quadrant and 3 tan A + 4 = 0, then the value of 2 cotA – 5 cos A + sin A is equal to

Accepted Answer

23/10

Answer

-53/10

Answer

37/10

Answer

7/10

Question 27

The value of cos² 48° – sin² 12° is

Accepted Answer

(√5+1)/8

Answer

(√5-1)/8

Answer

(√5+1)/5

Answer

(√5+1)/(2√2)

Question 28

If tan α = 1/7, tan β = 1/3, then cos 2α is equal to

Accepted Answer

sin 4β

Answer

sin 2β

Answer

sin 3β

Answer

cos 2β

Question 29

If tan θ = a/b, then b cos 2θ + a sin 2θ is equal to

Accepted Answer

b

Answer

a

Answer

a/b

Answer

None

Question 30

If for real values of x, cos θ = x + 1/x, then

Accepted Answer

No value of θ is possible

Answer

θ is an acute angle

Answer

θ is right angle

Answer

θ is an obtuse angle

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