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