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Question

The value of $$ \tan^{-1} \left( \dfrac {\sqrt3}{2} \right) + \tan^{-1} \left( \dfrac {1}{\sqrt3} \right) $$ is equal to :


A
tan1(53)
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B
tan1(23)
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C
tan1(12)
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D
tan1(133)
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E
tan1(523)
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Solution

The correct option is A $$ \tan^{-1} \left( \dfrac {5}{\sqrt3} \right) $$
The value of $$ \tan^{-1} \left( \dfrac {\sqrt3}{2} \right) + \tan^{-1} \left( \dfrac {1}{\sqrt3} \right) $$ is

$$ = \tan^{-1} \left( \dfrac {\dfrac {\sqrt3}{2} + \dfrac {1}{\sqrt3}}{1 - \dfrac {\sqrt3}{2} \times \dfrac {1}{\sqrt3}} \right) $$

$$ =\tan ^{ -1 } \left( \dfrac { \dfrac { 3+2 }{  2 \sqrt3}  }{ 1 - \dfrac{1}{2} }  \right)$$

$$ = \tan^{-1} \left( \dfrac {5}{\sqrt3} \right) $$

Option A is correct.

Mathematics

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