Answer
$A=5^{\circ}$
Work Step by Step
1. Secant and cosine are reciprocals
$\cos\theta=\frac{1}{\\sec\theta}$
2. Rewrite secant as cosine
$\cos(6A +5^{\circ})=\cos(4A+15^{\circ})$
3.Since the tangent values are equal, the angles themselves must be equal.
$6\theta -4\theta= 15-5$
$2\theta=10$
$\theta=5^{\circ}$
