TRIGONOMETRIC RATIOS AND TRIGONOMETRIC IDENTITIES (CDS)

Total Questions: 108

61. Solve the following equation [2016 (I) Morning Shift]

1.There are two values of θ satisfying the above equation.
2. θ = 60° is satisfied by the above equation.

Select the correct answer using the codes given below.

Correct Answer: (b) Only 2
Solution:

62. Which of the following is correct in respect of the equation 3 - tan²θ = α (1 - 3tan² θ)? (given that α is a real number.) [2016 (I) Morning Shift]

Correct Answer: (b)
Solution:

63. Solve the following equation [2016 (I) Morning Shift]

Correct Answer: (c) 1
Solution:

64. Consider the following statements [2015 (II) Evening Shift]

Correct Answer: (a) Only 1
Solution:

65. If x = a cos θ and y = b cot θ, then (ax⁻¹- by⁻¹) (ax⁻¹ + by⁻¹) is equal to [2015 (II) Evening Shift]

Correct Answer: (c) tan²θ
Solution:

66. Solve the following equation [2015 (II) Evening Shift]

Correct Answer: (b)
Solution:We have,

67. If tan(x + 40)° tan(x + 20)° tan(3x)° tan(70 - x)° tan(50 - x)° = 1, then the value of x is [2015 (II) Evening Shift]

Correct Answer: (c) 15
Solution:We have,


68. If θ is an acute angle and sin θ cos θ = 2cos³ θ - 1.5cos θ, then what is sin θ equal to? [2015 (II) Evening Shift]

Correct Answer: (a)
Solution:We have,

69. Consider the following statements [2015 (II) Evening Shift]

1. sin 66° is less than cos 66°
2. sin 26°is less than cos 26°

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

Correct Answer: (b) Only 2
Solution:

70. Solve the following equation [2015 (II) Evening Shift]

Correct Answer: (a) not possible
Solution:We have,