# Question #41efc

Jul 31, 2016

Prove trig identity

#### Explanation:

Left side of the equation:
$\sin \frac{t}{1 - \cos t}$
Right side of the equation.
$R S = \csc t + \cot t = \frac{1}{\sin t} + \cos \frac{t}{\sin t} = \frac{1 + \cos t}{\sin t} \left(1\right)$
Multiply the left side, both numerator and denominator, with (1 + cos t)
$L S = \frac{\left(\sin t\right) \left(1 + \cos t\right)}{\left(1 - \cos t\right) \left(1 + \cos t\right)} = \frac{\left(\sin t\right) \left(1 + \cos t\right)}{1 - {\cos}^{2} t} =$
$= \frac{\sin t \left(1 + \cos t\right)}{\sin} ^ 2 t = \frac{1 + \cos t}{\sin t} \left(2\right)$

Compare (1) and (2), we get LS = RS