I'm asked to prove something:

Question

If sinθ+cosθ=2√sinθ

then show that cosθ−sinθ=2√cosθ.

Answer 1

Given

squaring on both sides

From formula

we can write

We have formula

substitute in formula

By cancelling +1 and -1

Take common 2

We know that

Squaring on both sides we get

Hence it is proved that