Question

SinA+cosA whole square solvation

Answer 1

(1-sinA+cosA)2 = [(1-sinA) + cosA]2

=  (1-sinA)2 + cos2A + 2(1-sinA)cosA

=  1 + sin2A − 2sinA + cos2A + 2(1-sinA)cosA  

=  1 + (sin2A + cos2A) − 2sinA + 2(1-sinA)cosA  

=  1 + 1 − 2sinA + 2(1-sinA)cosA    [Since, sin2A + cos2A =1]

=  2 − 2sinA + 2(1-sinA)cosA

=  2(1 − sinA) + 2(1-sinA)cosA

=  2(1 − sinA)(1 + cosA)

= RHS

Answer 2

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