Question

If `(tan 3 theta - 1)/(tan 3 theta + 1) = sqrt3`, then the general value of θ is ______.

Options

• `("n"pi)/3 + pi/12`

• `("n"pi)/3 + (7pi)/36`

• `"n"pi + (7pi)/12`

• `"n"pi + (pi)/12`

Answer 1

`("n"pi)/3 + (7pi)/36`

Explanation:

`(tan 3 theta - 1)/(tan 3 theta + 1) = sqrt3`

`=> (tan 3theta - tan(pi/4))/(1 + tan 3 theta tan (pi/4)) = sqrt3`

`=> tan (3theta - pi/4) = tan  pi/3`

`=> 3theta - pi/4 = "n"pi + pi/3 => 3 theta`

`=> theta = ("n"pi)/3 + (7pi)/36`