Question

if cos 0 + sin 0 = √2 cos 0, then show that cos 0 - sin O = √2sinO​

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

I hope it may help you.