Question

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

Answer 1

Answer:

Let θ = x

cos x + sin x = √2 cos x

squaring on both side, we get......

cos2x + sin2x + 2cosxsinx = 2cos2x

2sinxcosx = 2cos2x - cos2x - sin2x

2sinxcosx = cos2x - sin2x

2sinxcosx = (cosx+sinx) (cosx - sinx)

2sinxcosx = (root2 cosx) (cosx - sinx)

2sinxcosx/root2 cosx = cosx - sinx

√2 sinx = cosx - sinx