TRIGONOMETRIC RATIOS AND TRIGONOMETRIC IDENTITIES (CDS)

Total Questions: 108

101. If sin θ cos θ =1/2, then what is sin⁶θ + cos⁶θ equal to? [2014 (I) Morning Shift]

Correct Answer: (d) 1/4
Solution:


102. If sec θ + tan θ = 2, then what is the value of sec θ? [2014 (I) Morning Shift]

Correct Answer: (d) 5/4
Solution:By trigonometric identity,

103. What is cosec(75° + θ) - sec(15° - θ) - tan (55° + θ) + cot(35° - θ) equal to? [2014 (I) Morning Shift]

Correct Answer: (b) 0
Solution:

104. If sin θ + 2cos θ = 1 where 0 < θ < π/2 then what is 2sin θ - cos θ equal to? [2014 (I) Morning Shift]

Correct Answer: (c) 2
Solution:sin θ + 2cos θ = 1 On squaring both sides, we get (sin θ + 2cos θ)² = 1

105. If cos x + sec x = 2 , then what cosⁿ x + secⁿ x equal to, where n is a positive integer? [2014 (I) Morning Shift]

Correct Answer: (a) 2
Solution:cos x + sec x = 2 ... (i)

106. What is sin 25° sin 35° sec 65° sec 55° equal to? [2014 (I) Morning Shift]

Correct Answer: (d) 1
Solution:

107. If tan 8θ = cot 2θ, where 0 < 8θ < π/2, then what is the value of tan 5θ? [2014 (I) Morning Shift]

Correct Answer: (b) 1
Solution:Given, tan 8θ = cot 2θ

108. If sin (A + B) = 1, where 0 < B < 45°, then what is cos (A - B) equal to? [2014 (I) Morning Shift]

Correct Answer: (a) sin 2B
Solution:∵ sin (A + B) = 1