Can Cos((Cos-1(2x-1))/2) Be Simplified to x?

[phymatter]

Homework Statement

is it possible that cos((cos^-1(2x-1))/2)) could be written only in terms of x , i mean by eliminating cos ans cos^-1 ?

Homework Equations

The Attempt at a Solution

 

[icystrike]

$$cos^{-1}(\frac{2x-1}{2}) = \theta$$

$$cos(\theta)=\frac{2x-1}{2}$$

Can u construct a triangle out of it? Labelling the sides.

Do u think that they will bring u back to where u were?

 

[tiny-tim]

hi phymatter!

you mean if cosA = 2x-1, what is cos(A/2)?

what is an equation relating cosA and cos(A/2)?

 

[Fragment]

icystrike, what you have is not exactly correct, as the original function is:

$$\cos(\frac{\cos^{-1}(2x-1)}{2})$$

 

[HallsofIvy]

$cos(x/2)= (1/2)\sqrt{1+ cos(x)}$ is the formula tiny-tim was referring to.

 

[phymatter]

thank everyone :)