find all values of x in the interval[0,2pie] that satisfies the equation 2+cos2x=3cosx

Question

directrix · Answer

Is this problem:

2 + cos(2x) = 3 cosx

or

2 + cos ² x = 3 cosx ?

anonymous · Answer

its the first one :)

anonymous · Answer

2 + cos(2x) = 3 cos x

directrix · Answer

Do you know the double angle formula for cosine?

directrix · Answer

@xyz10   ---> I'm here to help. Are you still here?

anonymous · Answer

am i going to replace cos 2x with 2 cos^2x-1  ?

directrix · Answer

I think we will but let's just start.

2 + cos(2x) = 3 cos x

2 + cos² x - sin²x = 3 cos x

directrix · Answer

We need to get this equation to one variable.

directrix · Answer

2 + cos² x - ( 1 - cos² x) = 3 cox x

Agree? Question?

anonymous · Answer

yes i agree  got it :)  thanks a lot

directrix · Answer

Do you want me to stop now or shall we solve the equation? It's your call.

anonymous · Answer

no thank you so much i think i got it from here . thank you :)

directrix · Answer

okay

anonymous · Answer

really appreciate your help