Q23 of 118 Page 5

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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