Question

If x = cosce θ + cot θ,.y = cosec θ – cot θ, then which of the following is true ?

A) x + y = 0

B) x – y = 0

C) x/y = 1

D) xy = 1

Answer 1

Correct option is: D) xy = 1

We have x = cosec \(\theta\) + cot \(\theta\) and y = cosec \(\theta\) - cot \(\theta\)

\(\therefore\) xy = (cosec \(\theta\) + cot \(\theta\)) . (cosec \(\theta\) - cot \(\theta\))

= \(cosec^2\theta - cot^2\theta\) (\(\because\) (a+b) (a-b) = \(a^2-b^2\))

= 1  (\(\because\) \(cosec^2\theta - cot^2\theta\) = 1)

Answer 2

Correct option is: D) xy = 1