Question 1183076: Find the solutions of the equation cos 2x + cos 𝑥 + 1 = 0 in the interval [0, 2𝜋).
Found 2 solutions by ikleyn, Solver92311:
Answer by ikleyn(52805)   (Show Source):
You can put this solution on YOUR website! .
Find the solutions of the equation cos 2x + cos 𝑥 + 1 = 0 in the interval [0, 2𝜋).
~~~~~~~~~~~~~~~~~~~
Your starting equation is
cos(2x) + cos 𝑥 + 1 = 0 (1)
Use cos(2x) = 2cos^2(x) - 1. Substitute it into the given equation. You will get
(2cos^2(x) - 1) + cos(x) + 1 = 0, or
2cos^2(x) + cos(x) = 0.
Factor left side
(2cos(x) + 1)*cos(x) = 0.
So, EITHER cos(x) = 0, giving x =  ,  ,
OR 2cos(x) + 1 = 0, giving cos(x) = -  , x =  ,  .
ANSWER. The solutions are , , , .
Solved.
Answer by Solver92311(821)  (Show Source):
|
|
|
