For the following find all exact solutions on 0 2 pi 2 cos2

For the following, find all exact solutions on [0, 2 pi] 2 cos^2 t + cos t = 1

Solution

2cos²t + cos t=1

2cos²t + cost-1=0

2cos²t +2cost-cost-1=0

2cos t(cost +1) -1(cos t+1)=0

(2cos t -1)(cos t+1)=0

2cos t-1=0    or cos t+1=0

cos t=1/2   or cos t=-1

Taking cos^-1on both sides

t= cos^-1(1/2)   or   t=cos^-1(-1)

t= pi/3,5pi/3    or t= pi

t=pi/3,pi,5pi/3