Question

If $\cos \theta =\frac{2x}{1+x^2}$, find the value of $\tan \theta$ and $\csc \theta$

Answer 1

$\cos \theta =\frac{2x}{1+x^2}$

$\sin \theta =\sqrt{1-{\cos }^2\theta }=\sqrt{1-\frac{4x^2}{(1+x^2{)}^2}}=\sqrt{\frac{x^4-2x^2+1}{(1+x^2{)}^2}}=\pm \frac{1-x^2}{1+x^2}$

$\tan \theta =\pm \frac{1-x^2}{1+x^2}$

$\text{cosec}\theta =\pm \frac{1+x^2}{1-x^2}$