# Math Help - Proving tangent reduction formula

1. ## 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

2. Originally Posted by Mike9182
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.
${\tan ^n (x)dx = \int {\tan ^{n - 2} (x)\left( {\sec ^2 (x) - 1} \right)dx} = \dfrac{{\tan ^{n - 1} (x)}}
{{n - 1}} - \int {\tan ^{n - 2} (x)dx} }$