SOLUTION: 2cos^2x + cosx = 0

Algebra ->  Trigonometry-basics -> SOLUTION: 2cos^2x + cosx = 0      Log On


   

Question 1033278: 2cos^2x + cosx = 0
Answer by ikleyn(52805) About Me  (Show Source):
You can put this solution on YOUR website!
.
2cos^2x + cosx = 0
~~~~~~~~~~~~~~~~~~~~ 

2cos%5E2%28x%29 + cos%28x%29 = 0,     (1)

cos%28x%29%2A%282cos%28x%29%2B1%29 = 0.      (2)

So, our equation (2) deploys in two equations:

1.  cosx) = 0  --->  x = pi%2F2+%2B+k%2Api,  k = 0, +/-1, +/-2, . . . (3)

and

2.  2cos(x) + 1 = 0  --->  cos(x) = -1%2F2  --->  x = 2pi%2F3+%2B+2k%2Api,  k = 0, +/-1, +/-2, . . . (4)

                                        and/or  x = 4pi%2F3+%2B+2k%2Api,  k = 0, +/-1, +/-2, . . . (5)

The union of the three sets (3) U (4) U (5) is the set of solutions of the original equation (1).