TRIGONOMETRIC RATIOS AND TRIGONOMETRIC IDENTITIES (CDS)

Total Questions: 108

91. What is (sin x cos y + cos x sin y) (sin x cos y-cos x sin y) equal to? [2014 (II) Evening Shift]

Correct Answer: (d) sin² x - sin² y
Solution:

92. What is (1 + cot x - cosec x) (1 + tan x + sec x) equal to? [2014 (II) Evening Shift]

Correct Answer: (b) 2
Solution:(1 + cot x - cosec x) (1 + tan x + sec x)

93. What is (cosec x - sin x) (sec x - cos x) (tan x + cot x) equal to? [2014 (II) Evening Shift]

Correct Answer: (d) 1
Solution:(cosec x - sin x) (sec x - cos x) (tan x + cot x)

94. Consider the following statements [2014 (II) Evening Shift]

1. sin 1°> sin 1
2. cos 1° < cos 1

Which of the above statement(s) is/are correct?

Correct Answer: (d) Neither 1 nor 2
Solution:We know that, sin 1° < sin 1 and cos 1 < cos 1°
Hence, neither Statement 1 nor 2 is correct.

95. If sin x + cosec x = 2 then what is sin⁹ x + cosec⁹ x equal to? [2014 (II) Evening Shift]

Correct Answer: (a) 2
Solution:Given, sin x + cosec x = 2 ...(i) On cubing Eq. (i) both sides, we get

96. If sin x + cos x = p and sin³ x + cos³ x = q, then what is p³ - 3p equal to? [2014 (II) Evening Shift]

Correct Answer: (b) -2q
Solution:Given, sin x + cos x = p ...(i) and sin³ x + cos³ x = q ...(ii)

97. The value of cos 25° − sin 25° is [2014 (I) Morning Shift]

Correct Answer: (a) positive but less than 1
Solution:Since, value of cosθ decreases, from 0° to 90° and at 45° it is equal to the value of sinθ.

Similarly, value of sinθ increases from 0 to 90° and at 45° it is equal to the value of cosθ.

For 0° < θ < 45 °, cos θ > sin θ So, value of cos 25° − sin 25° is always positive but less than 1.

98. In a right angled ∆ABC, right angle at B, if cos A = 4/5 , then what is sin C is equal to? [2014 (I) Morning Shift]

Correct Answer: (b) 4/5
Solution:In ∆ABC, cos A = 4/5

99. If α and β are complementary angles, then what is [2014 (I) Morning Shift]

Correct Answer: (c) sin α
Solution:Since, α and β are complementary angles.

100. If 2 cot θ = 3, then what is [2014 (I) Morning Shift]

Correct Answer: (c) 1/2
Solution:∵ 2 cot θ = 3