If sinx + cosx = m, then prove that sin6x + cos6x = 
where m2 ≤ 2
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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