sin^ 6 theta - cos^ 6 theta
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sin6θ+cos6θ+3sin2θcos2θ
⇒LHS=(sin2θ)3+(cos2θ)3+3sin2θcos2θ
Using, [a3+b3=(a+b)3−3ab(a+b)]
⇒LHS=(sin2θ+cos2θ)3−3sin2θcos2θ(sin2θ+cos2θ)3+3sin2θcos2θ
⇒LHS=1−3sin2θcos2θ+3sin2θcos2θ=1=RHS
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