Question

If cos 0 + sin 0 = √2 cos 0, show that (cos 0 – sin 0) = √2 sin .​

Answer 1

Answer :

Given,

cosθ+sinθ=2cosθ

squaring on both the sides, we get,

cos2θ+sin2θ+2sinθcosθ=2cos2θ

cos2θ−sin2θ=2cosθsinθ

(cosθ+sinθ)(cosθ−sinθ)=2cosθsinθ

2cosθ(cosθ−sinθ)=2cosθsinθ     [ Given cosθ+sinθ=2cosθ]

∴cosθ−sinθ=2sinθ   [henceproved]