Tanx=(2sqrt3/3)sinx What are all solutions?

1 Answer
Oct 29, 2015

Solve tan x = ((2sqrt3)/3).sin x

Ans: 0, pi, 2pi, +- pi/6

Explanation:

tan x = ((2sqrt3)/3).sin x
(sin x)/(cos x) = ((2sqrt3)/3).sin x
sin x = ((2sqrt3)/3).sin x.cos x
3sin x - (2sqrt3cos x.sin x) = 0
sin x (3 - 2sqrt3.cos x) = 0

a. sin x = 0 --> x = 0; x = pi; and x = 2pi
b. 3 - (2sqrt3)cos x = 0 --> (2sqrt3cos x) = 3
cos x = 3/(2sqrt3) = sqrt3/2 --> x = +- pi/6