Question

if cos theta +sin theta =root 2cos theta then prove that cos theta-sin theta =root 2 sin theta

Answer 1

Cos theta + sin theta = √ cos theta
Sin theta= √ cos theta - cos theta
Sin theta = cos theta ( √2-1)
Sin theta / √ 2-1= cos theta
Sin( √2+1)= cos theta
Putting the value of cos theta in
Cos theta - sin theta
Sin( √2+1) - sin theta
√ 2 sin theta - sin theta + sin theta
√ 2 sin theta