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Reduction Formulas (Secant and Cosecant)
THEOREM 3 Let m ≠ 1. Then (i) (ii) PROOF (ii) This can be done by integration by parts, but it is easier to use Theorem 2. Let n = 2  m. For m ≠ 2, n ≠ 0 and Theorem 2 gives whence For m = 2 the formula is already known, These reduction formulas can be used to integrate any even power of sec x or csc x, and to get the integral of any odd power of sec x or csc x in terms of ∫ sec x or ∫ csc x. We shall find ∫ sec x and ∫ csc x in the next chapter.


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