Question

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

Answer 1

$\begin{array}{c}L.H.S=\frac{1-\cos \theta }{1+\cos \theta }\\ multiplyanddivideby\left(1+\cos \theta \right)\\ \Rightarrow \left(\frac{1-\cos \theta }{1+\cos \theta }\right)\left(\frac{1+\cos \theta }{1+\cos \theta }\right)\\ \Rightarrow \frac{1-{\cos }^2\theta }{{\left(1+\cos \theta \right)}^2}\\ \Rightarrow {\left(\frac{\sin \theta }{1+\cos \theta }\right)}^2\end{array}$

Hence proved$.$