An alternative way in which the derivation could be done starts by substituting. Here we choose u xn because u0 nxn 1 is a simpler lower degree function. First we directly compute.
Putting the pieces together we get the reduction formula.
Using the power reduction formulas we can derive the following half-angle formulas. Putting the pieces together we get the reduction formula. Cos text 180text theta ldots ldots. This calculus video tutorial explains how to use the reduction formulas for trigonometric functions such as sine and cosine for integration.