# How do you simplify cos^2B / (1-sinB)?

Oct 24, 2015

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

#### Explanation:

Based on the definitions of $\sin$ and $\cos$ and on the Pythagorean Theorem
$\textcolor{w h i t e}{\text{XXX}} {\cos}^{2} \left(B\right) + {\sin}^{2} \left(B\right) = 1$
or
$\textcolor{w h i t e}{\text{XXX}} {\cos}^{2} \left(B\right) = 1 - {\sin}^{2} \left(B\right)$

$\textcolor{w h i t e}{\text{XXXXXXX}} = \left(1 - \sin \left(B\right)\right) \cdot \left(1 + \sin \left(B\right)\right)$

Therefore
color(white)("XXX")(cos^2(B))/(1-sin(B)) = (cancel((1-sin(B)))*(1+sin(B)))/(cancel((1-sin(B)))