Ncert Exemplar Trigonometry

Q1: If sinθ + cosecθ = 2, then sin²θ + cosec²θ is equal to

• 1
• 4
• 2
• None of these

Q2: If f(x) = cos² x + sec² x, then

• f(x) < 1
• f(x) = 1
• 2 < f(x) < 1
• f(x) ≥ 2

Q3: If tanθ = 1/2 , and tanx = 1/3, then the value of θ + x is

• π/6
• π
• 0
• π/4

Q4: Which of the following is not correct?

• sin θ = -1/5
• cos θ = 1
• sec θ = 1/2
• tan θ = 20

Q5: The value of tan 1° tan 2° tan 3° ... tan 89° is

• 0
• 1
• 1/2
• Not defined

Q6: The value of (1 – tan² 15°) / (1 + tan² 15°) is

• 1
• √3
• √3/2
• 2

Q7: The value of cos 1º cos 2º cos 3° ... cos 179° is

• 1/√2
• 0
• 1
• -1

Q8: If tan θ = 3 and θ lies in third quadrant, then the value of sin θ is

• 1/√10
• -1/√10
• -3/√10
• 3/√10

Q9: The value of tan 75° – cot 75° is equal to

• 2√3
• 2+√3
• 2-√3
• 1

Q10: Which of the following is correct?

• sin1°> sin 1
• sin 1°< sin 1
• sin 1° = sin 1
• sin 1° = (π/180) sin 1

Q11: If tan α = m/(m+1) , tan β = 1/(2m+1) , then α + β is equal to

• π/2
• π/3
• π/6
• π/4

Q12: The minimum value of 3 cosx + 4 sinx + 8 is

• 5
• 9
• 7
• 3

Q13: The value of tan 3A – tan 2A – tan A is equal to

• tan 3A tan 2A tan A
• – tan 3A tan 2A tan A
• tan A tan 2A – tan 2A tan 3A – tan 3A tan A
• None of these

Q14: The value of sin (45° + θ) − cos (45° – θ) is

• 2 cosθ
• 2 sinθ
• 1
• 0

Q15: The value of cot (π/4 + θ) cot (π/4 – θ) is

• -1
• 0
• 1
• Not defined

Q16: cos 2θ cos 2φ + sin² (θ – φ) – sin² (θ + φ) is equal to

• sin 2(θ + φ)
• cos 2(θ + φ)
• sin 2(θ – φ)
• cos 2(θ – φ)

Q17: The value of cos 12° + cos 84° + cos 156° + cos 132° is

• 1/2
• 1
• -1/2
• -1/8

Q18: If tan A = 1/2, tan B = 1/3, then tan (2A + B) is equal to

• 1
• 2
• 3
• 4

Q19: The value of sin (π/10) sin (13π/10) is

• 1/2
• -1/2
• -1/4
• 1

Q20: The value of sin 50° – sin 70° + sin 10° is equal to

• (√5+1)/8
• (√5-1)/8
• (√5+1)/5
• (√5+1)/(2√2)

Q21: If sin θ + cos θ = 1, then the value of sin 2θ is equal to

• 1
• 1/2
• 0
• -1

Q22: If α + β = π/4, then the value of (1 + tan α) (1 + tan β) is

• 1
• 2
• -2
• Not defined

Q23: If sin θ = -4/5 and θ lies in third quadrant then the value of cos (θ/2) is

• 1/5
• -1/√10
• -1/√5
• 1/√10

Q24: Number of solutions of the equation tan x + sec x = 2 cos x lying in the interval [0, 2π] is

• 0
• 1
• 2
• 3

Q25: The value of sin (π/18) + sin (π/9) + sin (π/6) + sin (π/9) is given by

• sin (7π/18) + sin (4π/9)
• sin (7π/18) + sin (π/9)
• cos (π/6) + cos (3π/7)
• cos (π/9) + sin (π/9)

Q26: 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

• -53/10
• 23/10
• 37/10
• 7/10

Q27: The value of cos² 48° – sin² 12° is

• (√5+1)/8
• (√5-1)/8
• (√5+1)/5
• (√5+1)/(2√2)

Q28: If tan α = 1/7, tan β = 1/3, then cos 2α is equal to

• sin 2β
• sin 4β
• sin 3β
• cos 2β

Q29: If tan θ = a/b, then b cos 2θ + a sin 2θ is equal to

• a
• b
• a/b
• None

Q30: If for real values of x, cos θ = x + 1/x, then

• θ is an acute angle
• θ is right angle
• θ is an obtuse angle
• No value of θ is possible