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Question

Prove thatsin6A+cos6A=1-3sin2Acos2A


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Solution

As we have sin6A+cos6A=1-3sin2Acos2A

Taking LHS sin6A+cos6A=(sin2A)3+(cos2A)3

We know that (a+b)3=a3+b3+3ab(a+b)

(sin2A)3+(cos2A)3=(sin2A+cos2A)33sin2Acos2A(sin2A+cos2A)As(sin2A+cos2A=1)So,=133sin2Acos2A(1)=1-3sin2Acos2A=R.H.S.

Thus, L.H.S.=R.H.S.

Hence, Proved


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