Question

Prove that (1 - sin theta + cos theta)^ = 2(1 + cos theta)(1 - sin theta)

Answer 1

» LHS :-

=> (1 - sinα + cosα)²

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» Using Algebraic Identify :-

(a+b+c)² = a²+b²+c²+2(ab)+2(bc)+2(ac)

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=> (1 - sinα + cosα)²

=> 1+sin²α+cos²α-2sinα-2sinα.cosα+2cosα

=> 1+1+2cosα-2sinα-2sinα.cosα
__________[since:- sin²a+cos²a = 1]

=> 2+2cosα-2sinα-2sinα.cosα

=> 2(1+cosα) -2sinα(1+cosα)

=> (2-2sinα).(1+cosα)

=> 2(1+cosα)(1-sinα)

=> RHS
-_______[PROVED]

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Answer 2

Hy friend see the attachment... hope you understand.