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Math Help - Proving tangent reduction formula

  1. #1
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    Proving tangent reduction formula

    How is this proven using integration by parts?

    \int{tan^n{x}}\,dx = \frac{tan^{n-1}{x}}{n-1} - \int{tan^{n-2}{x}}\,dx

    n does not equal 1
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  2. #2
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    Quote Originally Posted by Mike9182 View Post
    How is this proven using integration by parts?
    \int{tan^n{x}}\,dx = \frac{tan^{n-1}{x}}{n-1} - \int{tan^{n-2}{x}}\,dx
    Don't need parts.
    {\tan ^n (x)dx = \int {\tan ^{n - 2} (x)\left( {\sec ^2 (x) - 1} \right)dx}  = \dfrac{{\tan ^{n - 1} (x)}}<br />
{{n - 1}} - \int {\tan ^{n - 2} (x)dx} }
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