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Basic Inverse Trigonometric Functions

Prove that : ...

Question

Prove that :
${tan}^{- 1} 1 + {tan}^{- 1} 2 + {tan}^{- 1} 3 = π$

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Solution

Now,
${tan}^{- 1} 1 + {tan}^{- 1} 2 + {tan}^{- 1} 3$
$= \frac{π}{4} + {tan}^{- 1} \frac{2 + 3}{1 - 2.3}$
$= \frac{π}{4} + {tan}^{- 1} (- 1)$
$= \frac{π}{4} + \frac{3 π}{4}$
$= π$ .

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