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

Question

Prove The Half Angle 

Answer 1

Are you sure that you have presented the problem correctly?

 

It's well known that 1-cos²x = sin²x  ⇐ this is another form (equivalent) to the Left side of your equation.

 

The half-angle formula can be used to write cos (x/2) = √[½(1+cos x)].

Then we can write the following as equivalent to the Right side of your equation:

 

2 cos (x/2) = 2√[½(1+cos x)]   ⇐ this is another form of the Right side of your equation.

 

it's not making much sense to me!