Consider the integral where n is an integer. Using the trigonometric identity 1 + tan 2 x
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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.)
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