If [ 15^ + 1 75^ + 1 105^ + 195^ = 2a], then the value of [( a + 1 a )] is :

Question

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 :

Accepted Answer

$$\tan 15^\circ  + \tan 15^\circ  - \tan 15^\circ  + \tan 15^\circ $$

$$ = 2\tan 15^\circ $$

$$ = 2\left( {2 - \sqrt 3 } \right) = 2a \Rightarrow a = 2 - \sqrt 3 $$

$$\therefore$$ $${1 \over a} + a \Rightarrow \left( {2 + \sqrt 3 } \right) + \left( {2 - \sqrt 3 } \right) = 4$$

Solutions · 1