TRIGONOMETRIC RATIOS AND TRIGONOMETRIC IDENTITIES (CDS)

Total Questions: 108

81. The value of cosec² 67° + sec² 57° - cot² 33° - tan² 23° is [2015 (I) Morning Shift]

Correct Answer: (b) 2
Solution:

82. Consider the following statements [2015 (I) Morning Shift]

I. There exists atleast one value of x between 0 and π/2 which satisfies the equation sin⁴ x - 2sin² x - 1 = 0
II. sin 1.5 is greater than cos 1.5 .

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

Correct Answer: (b) Only II
Solution:

83. If sin x + cos x = c, then sin⁶ x + cos⁶ x is equal to [2015 (I) Morning Shift]

Correct Answer: (b)
Solution:Given, sin x + cos x = c


84. Consider the following statements [2015 (I) Morning Shift]

Correct Answer: (d) Neither I nor II
Solution:

85. At 8 : 30, the hour hand and the minute hand of a clock form an angle of [2015 (I) Morning Shift]

Correct Answer: (b) 75°
Solution:Here, n = 8, x = 30

86. Solve the following equation [2014 (II) Evening Shift]

Correct Answer: (a) cos θ - sin θ
Solution:

87. If tan θ + cot θ = 2, then what is sin θ + cos θ equal to? [2014 (II) Evening Shift]

Correct Answer: (c) √2
Solution:Given, tan θ + cot θ = 2

88. Solve the following equation [2014 (II) Evening Shift]

Correct Answer: (a) sin x
Solution:

89. Solve the following equation [2014 (II) Evening Shift]

Correct Answer: (b)
Solution:

90. Solve the following equation [2014 (II) Evening Shift]

Correct Answer: (b)
Solution: