Question

The value of ${\tan }^{-1}\left(\frac{\sqrt{3}}{2}\right)+{\tan }^{-1}\left(\frac{1}{\sqrt{3}}\right)$ is equal to :

• A. ${\tan }^{-1}\left(\frac{5}{\sqrt{3}}\right)$
• B. ${\tan }^{-1}\left(\frac{2}{\sqrt{3}}\right)$
• C. ${\tan }^{-1}\left(\frac{1}{2}\right)$
• D. ${\tan }^{-1}\left(\frac{1}{3\sqrt{3}}\right)$
• E. ${\tan }^{-1}\left(\frac{5}{2\sqrt{3}}\right)$

Answer 1

The correct option is A ${\tan }^{-1}\left(\frac{5}{\sqrt{3}}\right)$

The value of ${\tan }^{-1}\left(\frac{\sqrt{3}}{2}\right)+{\tan }^{-1}\left(\frac{1}{\sqrt{3}}\right)$ is

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

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

$={\tan }^{-1}\left(\frac{5}{\sqrt{3}}\right)$

Option A is correct.