Question

The question is attached

Answer 1

$cos(A - B) = cos A cos B + sin A sin B$

In this case, A is $\frac{\pi }{3}$ and B is $\frac{\pi }{5}$, so:

  $cos\frac{\pi}{3} cos\frac{\pi}{5} +sin\frac{\pi }{3} sin\frac{\pi }{5} =cos(\frac{\pi}{3} -\frac{\pi}{5} ) = cos\frac{2\pi}{15}$

Hope that helps!