Question

Rewrite the expression sin 6t cos 5t using a product identity.

Answer 1

\[
\sin x \cos y=\frac{\sin(x+y)+\sin(x-y)}2
\]

Answer 2

\[
\sin (\color{red}{5t}) \cos (\color{blue}{6t})=\frac{\sin(\color{red}{5t}+\color{blue}{6t})+\sin(\color{red}{5t}-\color{blue}{6t})}2
=\frac{\sin(11t)+\sin(-t)}{2}
\]