Question

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

Answer 1

$pcot\theta$ = $\sqrt{q^2-p^2}$

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

$\therefore$ $cose{c}^2\theta$ = 1 + $co{t}^2\theta$ = 1 + $\frac{q^2-p^2}{p^2}$ = $\frac{q^2}{p^2}$

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