Question

The value of ${\tan }^{-1}\frac{1}{2}+{\tan }^{-1}\frac{2}{11}$ is

• A. ${\tan }^{-1}\frac{3}{4}$
• B. ${\tan }^{-1}\frac{1}{4}$
• C. ${\tan }^{-1}\frac{1}{2}$
• D. None of these

Answer 1

Answer: (A)

${\tan }^{-1}\frac{1}{2}+{\tan }^{-1}\frac{2}{11}$
$={\tan }^{-1}\frac{\frac{1}{2}+\frac{2}{11}}{1-\frac{1}{2}\times \frac{2}{11}}={\tan }^{-1}\frac{15}{20}$
$={\tan }^{-1}\frac{3}{4}$