# Math Help - simplifying trig identity

1. ## simplifying trig identity

Hi. looking for help with simplifying an identity. The identity to be simplified is:
tan^4x + 2tan^2x + 1.

I'm confident that 2tan^2x + 1 will break down into:
tan^2x + tan^2x + 1 which equals tan^2x + sec^2x. But I'm not sure how to treat the tan^4 when converting to secant.

Any help will be much appreciate.
Mike Clemmons

2. Originally Posted by Mike Clemmons
Hi. looking for help with simplifying an identity. The identity to be simplified is:
tan^4x + 2tan^2x + 1.

I'm confident that 2tan^2x + 1 will break down into:
tan^2x + tan^2x + 1 which equals tan^2x + sec^2x. But I'm not sure how to treat the tan^4 when converting to secant.

Any help will be much appreciate.
Mike Clemmons
Note that the problem is in the form

$y^4+2y^2+1=(y^2+1)^2$

where $y=\tan(x)$

This should get you started.

3. Also recall that $\tan^2{\theta} + 1 = \sec^2{\theta}$.