Question

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

• A. $\frac{1}{\sqrt{5}}$
• B. $-\frac{2}{\sqrt{5}}$
• C. $\frac{2}{\sqrt{5}}$
• D. $-\frac{1}{\sqrt{5}}$

Answer 1

Answer: (C)

Let $co{t}^{-1}\left(-\frac{3}{4}\right)=a$
$\Rightarrow cota=-\frac{3}{4}$
$\therefore \frac{\pi }{2}<\alpha <\pi$
$\Rightarrow cos\alpha =-\frac{3}{5}$
$\Rightarrow 1-2si{n}^2\frac{\alpha }{2}=-\frac{3}{5}$
$\Rightarrow si{n}^2\frac{\alpha }{2}=\frac{4}{5}$
$\Rightarrow sin\frac{\alpha }{2}=\frac{2}{\sqrt{5}}$