Question

If cos θ+ sin θ=√2 cos θ, show that cos θ-sin θ=√2 sin θ

Answer 1

Let theta be A.

Given : cos A + sin A = root 2 cos A

Squaring on both sides,

(cos A + sin A)^2 = (root 2 cos A)^2

cos^2 A + 2 cos A sin A + sin^2 A = 2 cos^2 A

cos^2 A - 2 cos^2 A + 2 cos A sin A = -sin^2 A

-cos^2 A + 2 cos A sin A = -sin^2 A

cos^2 A - 2 cos A sin A =sin^2 A

Add sin^2 A on both sides

cos^2 A - 2 cos A sin A + sin^2 A = 2 sin^2 A

(cos A - sin A)^2 = 2 sin^2 A

cos A - sin A = root 2 sin A

Hope this helps......

Answer 2

●here is your answer●
●hope it helps●