Question

If $x=\sqrt{\frac{1-\cos \theta }{1+\cos \theta }}$, then $\frac{2x}{1-x^2}=$

• A. $\sin \theta$
• B. $\cos \theta$
• C. $\tan \theta$
• D. $\cot \theta$

Answer 1

Answer: (C)

$\tan \theta$

$x=\sqrt{\frac{1-\cos \theta }{1+\cos \theta }}=\sqrt{\frac{2{\sin }^2\frac{\theta }{2}}{2{\cos }^2\frac{\theta }{2}}}=\tan \frac{\theta }{2}$

Now, $\frac{2x}{1-x^2}=\frac{2\tan \frac{\theta }{2}}{1-{\tan }^2\frac{\theta }{2}}=\tan \theta$

Therefore, Answer is $\tan \theta$