Question

Can someone help me solve this trigonometric expression please? Thanks!

Answer 1

The correct answer is `2sec^2theta`.

Explanation:

The obvious first step here would be to put on a common denominator.

`1/(1 + sintheta) + 1/(1 - sintheta)`

`=(1 -sintheta)/((1 + sintheta)(1 -sintheta)) + (1 + sintheta)/((1 - sintheta)(1+ sintheta))`

`= (1 - sintheta + 1 + sintheta)/((1 + sintheta)(1 - sintheta))`

`= 2/(1 - sin^2theta)`

We know that `sin^2x + cos^2x = 1`, therefore:

`= 2/cos^2theta`

`= 2sec^2theta`

Hopefully this helps!