回復 62# XYZ 的帖子
第 8 題
\(\begin{align}
& \sin 5x \\
& =\sin x\cos 4x+\cos x\sin 4x \\
& =\sin x\left[ 1-2{{\left( \sin 2x \right)}^{2}} \right]+2\cos x\sin 2x\cos 2x \\
& =\sin x\left[ 1-2{{\left( 2\sin x\cos x \right)}^{2}} \right]+4{{\cos }^{2}}x\sin x\left[ 1-2{{\left( \sin x \right)}^{2}} \right] \\
& =\sin x\left[ 1-8{{\sin }^{2}}x\left( 1-{{\sin }^{2}}x \right) \right]+4\left( 1-{{\sin }^{2}}x \right)\sin x\left[ 1-2{{\left( \sin x \right)}^{2}} \right] \\
& =16{{\sin }^{5}}x-20{{\sin }^{3}}x+5\sin x \\
\end{align}\)
剩下的就簡單了…
