Question

(1 - sin A + cos A)^2 = 2 (1 - sin A) (1 + cos A) -​

Answer 1

$\:\: \underline{\underline{\bf{\large\mathfrak\red{~~Solution~~}}}}$

L.H.S.=(1-sinA+CosA)²

=(1-sinA)²+2(1-sinA)cosA+cos²A

=1-2sinA+sin²A+2cosA-2sinAcosA+cos²A

=1-2sinAcosA+1-2sinA+2cosA

=2-2sinAcosA-2sinA+2cosA

=2(1-sinAcosA-sinA+cosA)

R.HS.=2(1-sinA)(1+cosA)

=2(1-sinAcosA-sinA+cosA)

therefore..L.H.S=R.H.S(proved)

Hope this helps u....