# How do you simplify 1- (sin^2 theta/ (1-cos theta))= -cos theta?

Mar 28, 2018

#### Explanation:

Here,

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

$L H S = 1 - \left({\sin}^{2} \frac{\theta}{1 - \cos \theta} \times \frac{1 + \cos \theta}{1 + \cos \theta}\right)$

$= 1 - \frac{{\sin}^{2} \theta \left(1 + \cos \theta\right)}{1 - {\cos}^{2} \theta} \ldots . . \to \left(1 - {\cos}^{2} \theta = {\sin}^{2} \theta\right)$

=1-((cancelsin^2theta)(1+costheta))/(cancel(sin^2theta)

$= 1 - \left(1 + \cos \theta\right)$

$= 1 - 1 - \cos \theta$

$= - \cos \theta$

$= R H S$

Mar 28, 2018

$- \cos \theta$

#### Explanation:

Firstly take L.H.S.(left hand side),

i.e. $L H S = 1 - \left({\sin}^{2} \frac{\theta}{1 - \cos \theta}\right)$

$= 1 - \left[\frac{1 - {\cos}^{2} \theta}{1 - \cos \theta}\right]$

$= 1 - \left[\frac{{1}^{2} - {\left(\cos \theta\right)}^{2}}{1 - \cos \theta}\right]$

$= 1 - \left[\frac{\left(\left(1 + \cos \theta\right)\right) \left(\cancel{1 - \cos \theta}\right)}{\left(\cancel{1 - \cos \theta}\right)}\right]$

so after solving it will give,

$= 1 - \left(1 + \cos \theta\right)$

$= 1 - 1 - \cos \theta$

which will give,

$= - \cos \theta$

$= R H S$

hence proved.