# What is the answer of 1-cot²a=?

Jun 21, 2018

It helps to rewrite in terms of sine and cosine.

$1 - {\cot}^{2} a = 1 - {\cos}^{2} \frac{a}{\sin} ^ 2 a = \frac{{\sin}^{2} a - {\cos}^{2} a}{\sin} ^ 2 a = - \frac{{\cos}^{2} a - {\sin}^{2} a}{\sin} ^ 2 a = - \cos \frac{2 a}{\sin} ^ 2 a$

Hopefully this helps

Jun 21, 2018

$- \frac{\cos 2 a}{\sin} ^ 2 a$

#### Explanation:

$f \left(a\right) = \left(1 - {\cot}^{2} a\right) = \left(1 - \cot a\right) \left(1 + \cot a\right)$
$f \left(a\right) = \left(1 - \cos \frac{a}{\sin a}\right) \left(1 + \cos \frac{a}{\sin a}\right) =$
$f \left(a\right) = \left(\frac{\sin a - \cos a}{\sin a}\right) \left(\frac{\sin a + \cos a}{\sin a}\right)$
$f \left(a\right) = \frac{{\sin}^{2} a - {\cos}^{2} a}{\sin} ^ 2 a = - \frac{\cos 2 a}{{\sin}^{2} a}$