JEE MAIN - Mathematics (2023 - 30th January Morning Shift - No. 8)
If $$\tan 15^\circ + {1 \over {\tan 75^\circ }} + {1 \over {\tan 105^\circ }} + \tan 195^\circ = 2a$$, then the value of $$\left( {a + {1 \over a}} \right)$$ is :
$$5 - {3 \over 2}\sqrt 3 $$
$$4 - 2\sqrt 3 $$
2
4
Explanation
$$\tan 15^\circ + \tan 15^\circ - \tan 15^\circ + \tan 15^\circ $$
$$ = 2\tan 15^\circ $$
$$ = 2\left( {2 - \sqrt 3 } \right) = 2a \Rightarrow a = 2 - \sqrt 3 $$
$$\therefore$$ $${1 \over a} + a \Rightarrow \left( {2 + \sqrt 3 } \right) + \left( {2 - \sqrt 3 } \right) = 4$$
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