pre cal help Solve the equation 2 cos2 x cos x 1 0 0 LE x

pre cal help

Solve the equation 2 cos^2 x - cos x - 1 = 0, 0 LE x LE 2n. (Enter your answers as a comma-separated list. If there is no solution, enter NO SOLUTION.) x =

Solution

2cos^2x -cosx -1 =0

factorise: 2cos^2x -2cosx +cosx -1 =0

2cosx(cosx -1) +1(cosx -1) =0

(2cosx +1)(cosx -1)=0

cosx = -1/2 ----> x= pi - pi/3

x= pi+pi/3

x= 2pi/3 ,4pi/3

cosx =1

x= 0, 2pi

Solution : ( 0 , 2pi/3 , 4pi/3 , 2pi )