Consider the integral

where n is an integer. Using the trigonometric identity 1 + tan²x = sec²x, show that

and hence obtain the recurrence relation

Use this to find

(Recurrence relations of this type are often called reduction formulae, since they provide a systematic way of reducing the value of the parameter n so that a difficult integral may be reduced to an easier one.)

In 70/4 0 tan"x d.x