Question

If $pcot\theta$ = $\sqrt{q^2-p^2}$, then the value of $sin\theta$ is ___. ($\theta$ being an acute angle).

• A. $\frac{p}{q}$
• B. $\frac{q}{2p}$
• C. $\frac{q}{3p}$
• D. 0

Answer 1

The correct option is A

$\frac{p}{q}$

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

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

Using the identity, $cose{c}^2\theta$ = 1 + $co{t}^2\theta$
= 1 + $\frac{q^2-p^2}{p^2}$
= $\frac{q^2}{p^2}$

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