Question

$sin\left[\frac{1}{2}cot^{-1}\left(-\frac{3}{4}\right)\right]$ is equal to

• A. $\frac{1}{\sqrt5}$
• B. $-\frac{2}{\sqrt5}$
• C. $\frac{2}{\sqrt5}$
• D. $-\frac{1}{\sqrt5}$

Answer 1

Answer: (C)

Let $cot^{-1} \left(-\frac{3}{4}\right) = a $
$ \Rightarrow cot\, a = -\frac{3}{4}$
$\therefore \frac{\pi}{2} <\alpha < \pi $
$ \Rightarrow cos\, \alpha = -\frac{3}{5} $
$ \Rightarrow 1-2 sin^{2} \frac{\alpha}{2} = -\frac{3}{5}$
$ \Rightarrow sin^{2} \frac{\alpha}{2} = \frac{4}{5}$
$ \Rightarrow sin \frac{\alpha}{2} = \frac{2}{\sqrt{5}}$