For the last, you can start by using the following identities (derivable from the compound angle formulae):

1. sin(A + B) + sin(A - B) = 2 sin A cos B.

From which it follows that:

sin(x) + sin(3x) = 2 sin(2x) cos(x)

sin(5x) + sin(7x) = 2 sin(6x) cos(x)

2. cos(A + B) + cos(A - B) = 2 cos A cos B.

From which it follows that

cos(x) + cos(3x) = ........

cos(5x) + cos(7x) = ......