Question: what is the reduction formula?
Answer: Since the aim is to find a reduction formula, we require the integral on the right-hand side to involve cosx raised to a power less than n. We therefore set u=cosn−1x, since the derivative of u is u′=(n−1)cosn−2x(−sinx) (by the chain rule). Then set v′=cosx and integrate to obtain v=sinx.