# Question #4aefe

##### 1 Answer
Mar 20, 2016

It comes from the basic algebraic and trigonometric relationships shown below.

#### Explanation:

$\left(1 - \setminus \cos \left(x\right)\right) \left(1 + \setminus \cos \left(x\right)\right) = 1 - \setminus {\cos}^{2} \left(x\right)$ by difference of squares factorization

$= \setminus {\sin}^{2} \left(x\right)$ by Pythagorean identity

$= \frac{1}{\setminus} {\csc}^{2} \left(x\right)$ by definition of cosecant function as reciprocal of sine