Question

Evaluate (cosec A – 1) (cosec A + 1) (sec^2 A – 1).

(a) 0

(b) 1

(c) \(\frac {4}{3}\)

(d) \(\frac {3}{4}\)

The question was posed to me in an interview for job.

I would like to ask this question from Trigonometric Identities topic in portion Trigonometry of Mathematics – Class 10

Answer 1

The correct answer is (b) 1

For explanation: (cosec A – 1) (cosec A + 1) (sec^2 A – 1) = (cosec^2 A – 1) (sec^2 A – 1)

= cot^2A . tan^2 A

= \(\frac {1}{tan^2 A}\) . tan^2 A

= 1