# If sinx + cosx =

Given sinx + cosx = m

We have to prove that

Proof:

LHS = sin6x + cos6x

= (sin2x)3 + (cos2x)3

We know that a3 + b3 = (a + b) (a2 + b2- ab)

= (sin2x + cos2x)3 – 3sin2x cos2x(sin2x + cos2x)

= 1 – 3 sin2x cos2x

RHS

= 1 – 3 sin2x cos2x

LHS = RHS

Hence proved.

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