Evaluate $\int \cos \left(3x\right)\cos \left(5x\right)dx$ using the product-to-sum identity.

$\frac{1}{4}\sin \left(2x\right)+\frac{1}{16}\sin \left(8x\right)+C$

$\frac{1}{4}\cos \left(2x\right)+\frac{1}{16}\cos \left(8x\right)+C$

$\frac{1}{2}\sin \left(2x\right)-\frac{1}{8}\sin \left(8x\right)+C$

$\frac{1}{2}\cos \left(2x\right)-\frac{1}{8}\cos \left(8x\right)+C$