Question

If $pcot\theta$ = $\sqrt{q^2-p^2}$ where θ is an acute angle , then the value of $sin\theta$ is___.

• A. p/q
• B. q/2p
• C. q/3p
• D. 0

Answer 1

The correct option is A

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