(sinA + cosA) (1-sinAcosA)=sin^3A+cos^3A
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LHS =
(sinA + cosA)( 1- sinAcosA )
= (sinA + cosA )(sin²A + cos²A - sinA . cosA)
Since,
(x + y )(x²+y²-xy ) = x³ + y³
So,
(sinA + cosA )(sin²A + cos²A - sinA . cosA)
= sin³A + cos²A
= RHS.
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