# How do you perform addition or subtraction and use the fundamental identities to simplify 1/(1+cosx)+1/(1-cosx)?

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Feb 17, 2017

$\frac{1}{1 + \cos x} + \frac{1}{1 - \cos x} = 2 {\csc}^{2} x$

#### Explanation:

$\frac{1}{1 + \cos x} + \frac{1}{1 - \cos x}$

= $\frac{1 - \cos x + 1 + \cos x}{\left(1 + \cos x\right) \left(1 - \cos x\right)}$

= $\frac{2}{1 - {\cos}^{2} x}$

= $\frac{2}{\sin} ^ 2 x$

= $2 {\csc}^{2} x$

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