Kullanmak isteyen olursa: \begin{align*} \sin^6x+\cos^6x &= (\sin^2x)^3+(\cos^2x)^3\\[7pt] &=(\sin^2x+\cos^2x)^3-3\sin^2x\cos^2x(\sin^2x+\cos^2x)\\[7pt]&=1-3\frac{(2\sin x\cos x)^2}4\\[7pt]&=1-\frac34\sin^22x\\[7pt]&=1-\frac34\frac{1-\cos4x}2 \\[7pt]&=\frac18(5+3\cos4x)\end{align*}
\begin{align*} \sin^6x+\cos^6x &= (\sin^2x)^3+(\cos^2x)^3\\[7pt] &=(\sin^2x+\cos^2x)^3-3\sin^2x\cos^2x(\sin^2x+\cos^2x)\\[7pt]&=1-3\frac{(2\sin x\cos x)^2}4\\[7pt]&=1-\frac34\sin^22x\\[7pt]&=1-\frac34\frac{1-\cos4x}2 \\[7pt]&=\frac18(5+3\cos4x)\end{align*}