Answer
$\cos (4t)+\cos (6t)=2\cos 5t\cos t.$
Work Step by Step
Consider the function,
\begin{align*}
\cos (4t)+\cos (6t).
\end{align*}
According to the formula for sum of two cosines, we have
\begin{align*}
\cos A+ \cos B=2\cos \dfrac{A+B}{2}\cos \dfrac{A-B}{2}.
\end{align*}
Let $A=4t, B=6t$. Thus, we get
\begin{align*}
\cos 4t+ \cos 6t&=2\cos \dfrac{4t+6t}{2}\cos \dfrac{4t-6t}{2}\\
&=2\cos \dfrac{10t}{2}\cos \dfrac{-2t}{2}\\
&=2\cos 5t\cos t.
\end{align*}
Hence, $\cos (4t)+\cos (6t)=2\cos 5t\cos t.$
