Prove that : $(1 - sin θ + cos θ)^{2} = 2 (1 + cos θ) (1 - sin θ)$

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Prove that :

(1 - sin θ + cos θ)^{2} = 2 (1 + cos θ) (1 - sin θ)

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Text solutionVerified

L H S = (1 - s in θ + cos θ)^{2}

L H S = 1 + s i n^{2} θ + co s^{2} θ - 2 s in θ + 2 cos θ - 2 s in θ cos θ

L H S = 2 - 2 s in θ + 2 cos θ - 2 s in θ cos θ

L H S = 2 (1 - s in θ) + 2 cos θ (1 - s in θ)

L H S = 2 (1 - s in θ) (1 + cos θ) = R H S

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Question Text	Prove that : $(1 - sin θ + cos θ)^{2} = 2 (1 + cos θ) (1 - sin θ)$
Answer Type	Text solution:1
Upvotes	150