# If cot x =3 then what is the answer of this?

##  1/(1+cos x) + 1/(1-cos x) = ?

Feb 13, 2017

20

#### Explanation:

Expression $E = \frac{1}{1 + \cos x} + \frac{1}{1 - \cos x} =$
$\frac{\left(1 - \cos x\right) + \left(1 + \cos x\right)}{1 - {\cos}^{2} x} = \frac{2}{\sin} ^ 2 x$
Find ${\sin}^{2} x$ by using trig identity:
${\sin}^{2} x = \frac{1}{1 + {\cot}^{2} x}$
In this case:
${\sin}^{2} x = \frac{1}{1 + 9} = \frac{1}{10}$
There for
$E = \frac{2}{{\sin}^{2} x} = 20$