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Domain and Range of Basic Inverse Trigonometric Functions

Prove that ...

Question

Prove that ${tan}^{- 1} \frac{1}{2} + {tan}^{- 1} \frac{2}{11} = {tan}^{- 1} \frac{3}{4}$ .

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Solution

Now,
${tan}^{- 1} \frac{1}{2} + {tan}^{- 1} \frac{2}{11}$
$= {tan}^{- 1} \frac{\frac{1}{2} + \frac{2}{11}}{1 - \frac{1}{11}}$
$= {tan}^{- 1} \frac{\frac{15}{22}}{\frac{10}{11}}$
$= {tan}^{- 1} \frac{15}{20}$
$= {tan}^{- 1} \frac{3}{4}$ .

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