Question

$\cos(a) - \sin(a) = \sqrt{2 } \sin(a)$
Proved it​

Answer 1

Given,

cosθ + sinθ= √2cosθ

squaring on both the sides, we get,

cos^2 θ+ sin^2 θ + 2sinθ cosθ = 2cos^2 θ

cos^2 θ − sin^2 θ = 2cos θ sin θ

(cosθ+sinθ) (cosθ−sinθ) = 2cos θ sinθ

√2cos θ (cosθ−sinθ) = 2cos θ sin θ

[ Given cosθ+sinθ= √2cosθ]

∴ cos θ − sin θ = √2 sin θ

Hence proved