Question

If $p\cot \theta =\sqrt{q^2-p^2}$, then find the value of $\sin \theta$.

Answer 1

Given, $p\cot \theta =\sqrt{q^2-p^2}$

$\Rightarrow \cot \theta =\frac{\sqrt{q^2-p^2}}{p}$

$\because cose{c}^2\theta =1+{\cot }^2\theta \Rightarrow cose{c}^2\theta =1+\frac{q^2-p^2}{p^2}=\frac{q^2}{p^2}$

Hence, $cosec\theta =\frac{q}{p}$
$\because sin\theta =\frac{1}{cosec\theta }$

$\therefore \sin \theta =\frac{p}{q}$