Question

If ${\sin }^{-1}\alpha ={\tan }^{-1}\frac{3}{4}$, then $\alpha$ equals :

• A. $\frac{3}{5}$
• B. 1
• C. $\frac{2}{5}$
• D. $\frac{3}{4}$

Answer 1

Answer: (A)

Let ${\sin }^{-1}\alpha ={\tan }^{-1}\frac{3}{4}$ .......(1)
To find $\alpha$
Put ${\tan }^{-1}\frac{3}{4}=\theta \Rightarrow \tan \theta =\frac{3}{4}$
Now equation (i) becomes
${\sin }^{-1}\alpha =\theta \Rightarrow \alpha =\sin \theta$
$\Rightarrow \alpha =\frac{1}{cosec\theta }=\frac{1}{\sqrt{1+{\cot }^2\theta }}$
$\Rightarrow \alpha =\frac{1}{\sqrt{1+\frac{1}{{\tan }^2\theta }}}=\frac{1}{\sqrt{1+{\left(\frac{4}{3}\right)}^2}}$
$\Rightarrow \alpha =\frac{3}{5}$