Question

(1 + cosec⁡ θ) (1 – cosec⁡ θ) + cot^2⁡ θ is _____

(a) Cot ⁡θ

(b) 0

(c) 1

(d) Tan ⁡θ

I have been asked this question during a job interview.

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

Answer 1

Correct answer is (b) 0

For explanation: (1 + cosec⁡ θ) (1 – cosec θ) + cot^2 ⁡θ = (1 – cosec^2 θ) + cot^2 θ

= -cot^2⁡ θ + cot^2⁡ θ     (∵ cosec^2 A – cot^2 A = 1)

= 0