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Theorems on Integration

Prove that : ...

Question

Prove that :
${tan}^{- 1} \frac{1}{2} + {tan}^{- 1} 2 = \frac{π}{2}$

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Solution

Now,
${tan}^{- 1} \frac{1}{2} + {tan}^{- 1} 2$
$= {tan}^{- 1} \frac{\frac{1}{2} + 2}{1 - \frac{1}{2} \times 2}$
$= {tan}^{- 1} \frac{\frac{5}{2}}{0}$
$= \frac{π}{2}$ .

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