If sin x +cos x= root2* cos x, prove that cos x -sin x= root2* sin x.

Question

If sin x + cos x =√2cos x then prove that cos x - sin x = √2 sin x

Answer 1

Solution:
cos x + sinx = √ 2 cos x , then (√2 -1 ) cos  x = sin x
on multiplying both sides by (√2+1) , we get
(√2+1)(√2-1) cos x  =  (√2+ 1) sin x
⇒ cos x = √2 sin x + sin x
⇒ cos x -sin x = √ 2 sin x