Question

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

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

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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