Question

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

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

Answer 1

The correct option is A

$\frac{p}{q}$

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

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

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

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