Question

If cosθ + sinθ = root 2 cosθ, show that cosθ sinθ = root 2 sinθ.

Answer 1

cosθ+sinθ=√2cosθ
or, sinθ=√2cosθ-cosθ
or, sinθ=cosθ(√2-1)
or, sinθ=cosθ[(√2-1)(√2+1)/(√2+1)]
or, sinθ=cosθ(2-1)/(√2+1)
or, √2sinθ+sinθ=cosθ
or, sinθ-cosθ=-√2sinθ
or, cosθ-sinθ=√2sinθ

Answer 2

cosθ+sinθ=√2cosθ

or, sinθ=√2cosθ-cosθ

or, sinθ=cosθ(√2-1)

or, sinθ=cosθ[(√2-1)(√2+1)/(√2+1)]

or, sinθ=cosθ(2-1)/(√2+1)

or, √2sinθ+sinθ=cosθ

or, sinθ-cosθ=-√2sinθ

or, cosθ-sinθ=√2sinθ