Answer :
LHS
We know that
We know that a3 + b3 = (a + b) (a2 + b2- ab)
= 1 – (sin2x + cos2x) + sinx cosx
We know that sin2x + cos2x = 1.
= 1 – 1 + sinx cosx
= sinx cosx
= RHS
Hence proved.
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