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

1 Answer
Nghi N.
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#

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