# Write this expression in terms of sine and cosines and simplify? (Cosßtanß+1) (Sinß-1)

Mar 27, 2018

It simplifies to $- {\cos}^{2} \beta$.

#### Explanation:

Recall that $\tan \beta = \sin \frac{\beta}{\cos} \beta$.

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

$= \left(\sin \beta + 1\right) \left(\sin \beta - 1\right)$

$= {\sin}^{2} \beta - 1$

Recall that ${\sin}^{2} x + {\cos}^{2} x = 1$.

$= - {\cos}^{2} \beta$

Hopefully this helps!