Question:
cos theta sin theta=root2costheta show thatcos theta-sintheta=root2sintheta
Answer:
Given cos θ + sin θ = √2*cos θ
Squaring on both side, we get
=> cos2 θ + sin2 θ + 2*cos θ*sin θ = 2*cos2 θ
=> 2*cos θ*sin θ = 2*cos2 θ - cos2 θ - sin2 θ
=> 2*cos θ*sin θ = cos2 θ - sin2 θ
=> 2*cos θ*sin θ = (cos θ - sin θ)*(cos θ + sin θ)
=> 2*cos θ*sin θ = (cos θ - sin θ)*(√2*cos θ)
=> 2*cos θ*sin θ/(√2*cos θ) = (cos θ - sin θ)
=> √2*sin θ = cos θ - sin θ
=> cos θ - sin θ = √2*sin θ
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