SOLUTION: cos 2 theta + 3 cos theta =1

Algebra ->  Trigonometry-basics -> SOLUTION: cos 2 theta + 3 cos theta =1      Log On


   

Question 1112195: cos 2 theta + 3 cos theta =1
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
cos 2 x + 3 cos x =1
2cos^2 x -1+3 cos x=1
2 cos^2x+3 cos x -2=0
(2 cos x-1)(cos x +2)=0
2 cos x=1 (cos x cannot be -2)
cos x= (1/2)
x=pi/3, 5 pi/3 ANSWER
cos 2 pi/3+ 3 cos pi/3=-0.5+3(0.5)=1
cos 10 pi/3+ 3 cos 5 pi/3=-0.5+3(0.5)=1