# Fundamental identities to simplify

• Feb 20th 2010, 11:42 PM
UserPanther
Fundamental identities to simplify
simplify:
(tan^2theta)/(sec^2theta)

still trying to find how to start out haha but cant seem to find out if anyone can help im really struggling with this...
• Feb 20th 2010, 11:55 PM
Prove It
Quote:

Originally Posted by UserPanther
simplify:
(tan^2theta)/(sec^2theta)

still trying to find how to start out haha but cant seem to find out if anyone can help im really struggling with this...

Remember that $\displaystyle \sec^2{\theta} = \tan^2{\theta} + 1$

So $\displaystyle \tan^2{\theta} = \sec^2{\theta} - 1$.

Also recall that $\displaystyle \sin^2{\theta} + \cos^2{\theta} = 1$.

Therefore

$\displaystyle \frac{\tan^2{\theta}}{\sec^2{\theta}} = \frac{\sec^2{\theta} - 1}{\sec^2{\theta}}$

$\displaystyle = 1 - \frac{1}{\sec^2{\theta}}$

$\displaystyle = 1 - \cos^2{\theta}$

$\displaystyle = \sin^2{\theta}$.
• Feb 21st 2010, 12:12 AM
UserPanther
Thank you so much i see how you did it i just need to get used to using all the identities