Question

please help!!!! Solve for x:
cos(X) + cos(2x) = -1

Answer 1

DO YOU KNOW THE FORMULA OF cos(2x) ????

Answer 2

Here's a cheat sheet if you need it.
http://tutorial.math.lamar.edu/pdf/Trig_Cheat_Sheet.pdf

Answer 3

what do you mean?

Answer 4

He means if you change cos(2x) to some function of cos(x), then you can more easily solve for cos(x).

Answer 5

x=-1/2 cos^(-1)(-1-cos(X))

Answer 6

and another solution is x=1/2 cos^(-1)(-1-cos(X))

Answer 7

but what is x then??

Answer 8

\[\cos(x)+\cos(2x)=-1\]
\[\cos(x)+\cos^{2}(x)-\sin^{2}(x)+1=0\]
\[\cos(x)+2\cos^{2}(x)=0 ...since...1-\sin^{2}(x)=\cos^{2}(x)\]
\[\cos(x)=0...or...1+2\cos(x)=0\]
Can U find x from here ?

Answer 9

What interval are you solving over?
There are four solutions between 0 and 2π.

Answer 10

yes i can solve x from here...thanks you guys for helping!!