Fundamental identities to simplify

**UserPanther** · February 20th 2010, 11:42 PM

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...

**Prove It** · February 20th 2010, 11:55 PM

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

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

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

Therefore

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

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

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

$= \sin^2{\theta}$ .

**UserPanther** · February 21st 2010, 12:12 AM

Thank you so much i see how you did it i just need to get used to using all the identities

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