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Prove that: (1 – sinθ + cosθ)^2 = 2(1 + cosθ)(1 – sinθ) - Mathematics

Sum

Prove that: `(1 – sinθ + cosθ)^2 = 2(1 + cosθ)(1 – sinθ)`

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Solution

`(1 – sinθ + cosθ)^2`

`= 1 + sin^2 θ + cos^2 θ – 2sinθ + 2cosθ – 2sinθcosθ`

= 2 – 2sinθ + 2cosθ – 2sinθcosθ

= 2 (1 – sinθ) + 2 cosθ (1 – sinθ)

= 2(1 – sinθ)(1 + cosθ) = RHS

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