Question

(1-sinx+cosx)^2=2(1+cosx)(1-sinx)

Answer 1

LHS = (1-sinx+cosx)²

= 1²+sin²x+cos²x-2sinx-2sinxcosx+2cosx

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We know the algebraic identity:

i)(a+b+c)²=a²+b²+c²+2ab+2bc+2ca

ii) sin²x+cos²x = 1

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= 1+1-2sinx -2-2sinxcosx+2cosx

= 2-2sinx-2sinxcosx+2cosx

= 2(1-sinx)+2cosx(-sinx+1)

= 2(1-sinx)(1+cosx)

=RHS

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