Question

Show that $\sqrt{\frac{1+\sin \theta }{1-\sin \theta }}=\frac{1+\sin \theta }{\cos \theta }$

Answer 1

LHS:$\sqrt{\frac{1+sin\theta }{1-sin\theta }}=\sqrt{\frac{1+sin\theta }{1-sin\theta }\times \frac{1+sin\theta }{1+sin\theta }}$
$=\sqrt{\frac{(1+sin\theta {)}^2}{1-si{n}^2\theta }}$
$=\sqrt{\frac{(1+sin\theta {)}^2}{co{s}^2\theta }}$
$=\frac{1+sin\theta }{cos\theta }$