Question

answer this question in detail i will mark u as brainliest....

but in detail

Answer 1

Here, I am writing theta as A.

$Given : \frac{cosA}{1 - tanA} + \frac{sinA}{1 - cotA}$

$= > \frac{cosA}{1 - \frac{sinA}{cosA}} + \frac{sinA}{1 - \frac{cosA}{sinA}}$

$= > \frac{cosA}{\frac{cosA - sinA}{cosA}} + \frac{sinA}{\frac{sinA - cosA}{sinA}}$

$= > \frac{cos^2A}{cosA-sinA} + \frac{sin^2A}{sinA - cosA}$

$= > \frac{cos^2A}{cosA - sinA} - \frac{sin^2A}{cosA - sinA}$

$= > \frac{cos^2A - sin^2A}{cosA - sinA}$

We know that a^2 - b^2 = (a + b)(a - b)

$= > \frac{(cosA - sinA)(cosA + sinA)}{cosA - sinA}$

= > sinA + cosA

Hope this helps!

Answer 2

Hey friend here is your answer...

HOPE THIS HELPS :)