Solve the equation cos x Squareroot 3 cos x tan x Square

Solve the equation. cos x + Squareroot 3 = - cos x tan x + Squareroot 3 = 0

Solution

a. cos x + sqrt3 = - cos x

-2cos x= sqrt3

cos x= -(sqrt3)/2

x=cos^-1(-(sqrt3)/2) = 5pi/6, 7pi/6             in [0,2pi)

b. tan x + sqrt3=0

tan x= - sqrt3

    x= tan^-1(- sqrt3)

x= 2pi/3, 5pi/3         in      [0,2pi)