Trig3.2

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Show that \cos^6 A-\sin^6 A=\cos 2A[1-\frac{\sin^2 2A}{4}]\,

LHS=[\cos^2 A]^3-[\sin^2 A]^3\,

(cos^2 A-\sin^2 A)[(\cos^2 A)^2+\cos^2 A \sin^2 A+(\sin^2 A)^2]\,

\cos 2A[(\cos^2 A+\sin^2 A)^2-\sin^2 A \cos^2 A]\,

\cos 2A[1-\frac{1}{4}(4\sin^2 A \cos^2 A)]\,

\cos 2A[1-\frac{\sin^2 2A}{4}]\,=RHS


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