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Question

The value of $$\tan^{-1}2+\tan^{-1}3+\tan^{-1}4$$ is equal to 


A
πtan135
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B
π+tan153
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C
πtan153
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D
π+tan135
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Solution

The correct option is D $$\displaystyle \pi+\tan^{-1}\frac{3}{5}$$
$$\displaystyle \tan ^{ -1 }{ 2 } +\tan ^{ -1 }{ 3 } +\tan ^{ -1 }{ 4 } =\pi +\tan ^{ -1 }{ \left( \frac { 2+3 }{ 1-2.3 }  \right)  } +\tan ^{ -1 }{ 4 } \quad \left( \because \quad 2.3>1 \right) \\ \displaystyle =\pi -\tan ^{ -1 }{ 1 } +\tan ^{ -1 }{ 4 } \\ \displaystyle =\pi +\tan ^{ -1 }{ \left( \frac { 4-1 }{ 1+1.4 }  \right)  } \\ \displaystyle =\pi +\tan ^{ -1 }{ \frac { 3 }{ 5 }  } $$

Mathematics

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