Solve the equation on the interval 0

Solve the equation on the interval 0<=x<2.

cos (2x) = - sqrt(3)/2

Solution

cos(2x) =-sqrt(3)/2 ; 0<=x <2pi

2x = cos^-1(-sqrt(3)/2)

2x = 5pi/6 +2kpi

x = 5pi/12 +kpi = (5pi +12kpi)/12

2x = 7pi/6 +2kpi

x = 7pi/12 +kpi = (7pi +12kpi)/12

k =0 x = 5pi/12

k =1 ;x = 17pi/12

k=0 x =7pi/12

k=1 ; x = 19pi/12

Solution : x = 5pi/12 , 17pi/12, 7pi/12 , 19pi/12