TRIGONOMETRIC RATIOS AND TRIGONOMETRIC IDENTITIES (CDS)

Total Questions: 108

51. Solve the following equation [2016 (II) Evening Shift]

Correct Answer: (a)
Solution:

52. Consider the following [2016 (II) Evening Shift]

I. sin 1º > sin 1º
II. cos 1º < cos 1º
III. tan 1° > tan 1º

Which of the above are not correct?

Correct Answer: (d) I, II and III
Solution:We know that,

53. Solve the following equation [2016 (II) Evening Shift]

Correct Answer: (c) 45°
Solution:Given,


54. Consider the following [2016 (II) Evening Shift]

Correct Answer: (d) I, II and III
Solution:


55. What is the value of tan 1° tan 2° tan 3° tan 4° ..... tan 89°? [2016 (II) Evening Shift]

Correct Answer: (b) 1
Solution:We have, tan 1° tan 2° tan 3° tan 4° ..... tan 89°

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

Correct Answer: (c)
Solution:We have, tan θ + cot θ = 4/√3

57. Consider the following statements [2016 (I) Morning Shift]

1. There exists a positive real number m such that, cos x = 2ᵐ⁺¹
2. mn ≥ m + n for all m, n belonging to set of natural numbers.

Which of the above statements is/are correct?

Correct Answer: (d) Neither 1 nor 2
Solution:1. As cosx lies between -1 and 1, then cosx = 2ᵐ⁺¹ does not exist for positive value of m.

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

Correct Answer: (d) 2cos²θ
Solution:



59. Consider the following [2016 (I) Morning Shift]

Correct Answer: (c) Both 1 and 2
Solution:


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

Correct Answer: (b) 1
Solution:We have, p = cot θ + tan θ