How can the reduction formula be used to find the integral of tan^4 x?

[silicon_hobo]

Homework Statement

a)Prove the reduction formula:

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

Hint: first write tan^n x as tan^{n-2} \ x\ tan^2\ x and the rewrite using tan^2\ x+1=sec^2\ x.

b) Use the formula twice to find \int\ tan^4\ dx

The Attempt at a Solution

I not sure what they're asking for when they say "prove". How should I begin with this one? Thanks

 

[Vid]

Use methods of integration to show the left side equals the right. From the form of the right side, it should be pretty obvious which method to use.