find solution cos x + 1 = 2 cos x

Question

I need to fugure this out

Answer 1

cos x + 1 = 2 cos x

 

Subtract cos x from both sides...

 

1 = cos x

 

So x is a number whose cosine is 1.

 

The question doesn't restrict the answer to any particular range, so they must be asking for all solutions.

 

cos x = 1 when x = 0, plus any integer multiple of 2π.  So you can say that x = 2πn, where n can be any integer.