Cosθ + sinθ = root 2 cosθ, show that cosθ sinθ = root2 sinθ.
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cosθ+sinθ=√2cosθ
or, sinθ=√2cosθ-cosθ
or, sinθ=cosθ(√2-1)
or, sinθ=cosθ(√2-1)(√2+1)/(√2+1)
or, √2sinθ+sinθ=cosθ{(√2)²-(1)²}
or, √2sinθ+sinθ=cosθ(2-1)
or, sinθ-cosθ=-√2sinθ
or, cosθ-sinθ=√2sinθ (Proved)
or, sinθ=√2cosθ-cosθ
or, sinθ=cosθ(√2-1)
or, sinθ=cosθ(√2-1)(√2+1)/(√2+1)
or, √2sinθ+sinθ=cosθ{(√2)²-(1)²}
or, √2sinθ+sinθ=cosθ(2-1)
or, sinθ-cosθ=-√2sinθ
or, cosθ-sinθ=√2sinθ (Proved)
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