<html><head><meta name="color-scheme" content="light dark"></head><body><pre style="word-wrap: break-word; white-space: pre-wrap;">\documentclass[a4paper,12pt]{article}
\newcommand{\ds}{\displaystyle}
\newcommand{\pl}{\partial}
\parindent=0pt
\begin{document}


{\bf Question}

Prove that $$16\cos^4\theta\sin\theta = \sin5\theta + 3\sin
3\theta + 2\sin \theta$$

\vspace{.25in}

{\bf Answer}

Use $\sin 5\theta + 3\sin 3\theta + 2\sin\theta = Im \{(c+is)^5 +
3(c+is)^3 + 2(c+is)\}$

Expand and take imaginary parts, using the fact that $\ds c^2 +
s^2 = 1$

\end{document}
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