# Prove the Reduction Forumla

1. Mar 27, 2008

### silicon_hobo

1. The problem statement, all variables and given/known data
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 $$\int\ tan^4\ dx$$

3. 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

2. Mar 27, 2008

### 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.