# Thread: Prove the identity

1. ## [Solved] Prove the identity

Hey, could some one help me prove the following identity?

$\displaystyle \sec \theta + \csc \theta - \cos \theta - \sin \theta = \sin \theta * \tan \theta + \cos \theta * \cot \theta$

2. Originally Posted by gordo151091
Hey, could some one help me prove the following identity?

$\displaystyle \sec \theta + \csc \theta - \cos \theta - \sin \theta = \sin \theta * \tan \theta + \cos \theta * \cot \theta$
Just combine the terms on the LHS, creating common denominators...

$\displaystyle \displaystyle\frac{1}{Cos\theta}+\frac{1}{Sin\thet a}-\left(Cos\theta+Sin\theta\right)=\frac{Sin\theta+C os\theta}{Cos\theta\,Sin\theta}-\frac{Cos^2\theta\,Sin\theta+Sin^2\theta\,Cos\thet a}{Cos\theta\,Sin\theta}$

$\displaystyle =\displaystyle\frac{Sin\theta\left(1-Cos^2\theta\right)+Cos\theta\left(1-Sin^2\theta\right)}{Sin\theta\,Cos\theta}=\frac{Si n^3\theta+Cos^3\theta}{Sin\theta\,Cos\theta}$

Simplifying that is all that's required.

3. Thanks! I finally saw the mistake I was repeating over and over...