Question

$\cos \theta =\frac{2x}{1+x^2}$, find the value of $\sin \theta$ and $\cot \theta$, [given $x^2<1]$.

Answer 1

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

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

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