question_answer

Consider\[f(x)={{\tan }^{-1}}\left( \sqrt{\frac{1+\sin x}{1-\sin x}} \right),\]\[x\in \left( 0,\frac{\pi }{2} \right)\]. A normal to y = f(x) at \[x=\frac{\pi }{6}\]also passes through the point:

A)  \[\left( 0,\frac{2\pi }{3} \right)\]

B)  \[\left( \frac{\pi }{3},0 \right)\]

C)  \[\left( \frac{\pi }{4},0 \right)\]                

D)  \[\left( 0,\frac{\pi }{4} \right)\]