Question

If `1/(1 + sin θ) + 1/(1 - sin θ) = k sec^2θ`, then the value of k is ______.

Answer 1

If `1/(1 + sin θ) + 1/(1 - sin θ) = k sec^2θ`, then the value of k is 2.

Explanation:

`1/(1 + sinθ) + 1/(1 - sinθ) = ((1 - sinθ) + (1 + sinθ))/(1 - sin^2θ)` 

= `2/(cos^2θ)`

= 2 sec²θ

So k = 2.