Question

If cosx+sinx=root2cosx, then prove that cosx-sinx=root 2sinx

Answer 1

os 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.