How do you solve 3tan^2x = 1?

1 Answer
Nov 14, 2015

x = 30^o , 150^o , 210^0 , 330^0

Explanation:

The given quadratic equation = 3tan^2 = 1

tan^2x = 1/3

Finding square root on both sides

tanx = +- 1/sqrt3

Taking +ve value

tanx = 1/sqrt3

tanx = tan30^0

x = 30^0

since x is positive, x is positive in first or third quadrant

So, x = 30^0 or 180^0 + 30^0
= 30^0 or 210^0

Again taking -ve value

tanx = -1/sqrt3

Since tan will have negative value in second and fourth quadrant

x = 180-30 or 360-30

x =150^o or 330^o

Hence x = 30^o , 150^o , 210^0 , 330^0