Answer
$\theta=1^{\circ}$
Work Step by Step
1. Secant and cosine are reciprocals
$\sec\theta=\frac{1}{\cos\theta}$
2. Rewrite secant as cosine
$\cos(5\theta +3^{\circ})=\cos(2\theta+6^{\circ})$
3.Since the cosine values are equal, the angles themselves must be equal.
$5\theta -2\theta= 6-3$
$3\theta=3$
$\theta=1^{\circ}$
