Question

If ${\sin }^{-1}\frac{1}{2}={\tan }^{-1}x$ then $x=$

• A. $\sqrt{3}$
• B. $\frac{1}{\sqrt{3}}$
• C. $\frac{1}{\sqrt{2}}$
• D. None of these

Answer 1

The correct option is B

$\frac{1}{\sqrt{3}}$

Finding the value of $x$:

Given, ${\sin }^{-1}\frac{1}{2}={\tan }^{-1}x...\left(1\right)$

Convert ${\sin }^{-1}x$ in terms of ${\tan }^{-1}$.

${\sin }^{-1}\frac{1}{2}={\tan }^{-1}\frac{1}{\sqrt{3}}....\left(2\right)$

Equating$\left(1\right)\&$ $\left(2\right)$ we get:

$x=\frac{1}{\sqrt{3}}$

Hence, option B is correct.