Answer
The solutions of the equation is $\theta =\pi +2n\pi $, where n is any integer.
Work Step by Step
$\begin{align}
& 7\cos \theta +9=-2\cos \theta \\
& 7\cos \theta +2\cos \theta =-9 \\
& 9\cos \theta =-9 \\
& \cos \theta =-1
\end{align}$
$\cos \pi =-1$, and the solution of $\cos \theta =-1$ in [0, $2\pi $ ) is:
$\theta =\pi $
The period of the tangent function is $2\pi $, and the solutions are given by:
$\theta =\pi +2n\pi $,
where n is any integer.
