Question

Упростите выражение:

${sin}^{3} 3 \alpha \times cos3 \alpha - {cos}^{3} \alpha \times sin3 \alpha$
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Answer 1

$Sin^{3} 3\alpha*Cos3\alpha-Cos^{3}3\alpha*Sin3\alpha=Sin3\alpha Cos3\alpha\underbrace{(Sin^{2}3\alpha-Cos^{2}3\alpha)}_{-Cos6\alpha}=\\\\=\frac{1}{2}*\underbrace{(2Sin3\alpha Cos3\alpha}_{Sin6\alpha}*(-Cos6\alpha)=-\frac{1}{2}Sin6\alpha Cos6\alpha=\\\\=-\frac{1}{2}*\frac{1}{2}\underbrace{(2Sin6\alpha Cos6\alpha)}_{Sin12\alpha}=\boxed{-0,25Sin12\alpha}$