Question

If cos θ + sin θ = √(2)cos θ, prove that : cos θ - sin θ = ± √(2)sin θ.

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