Can the sum of square cosines be expressed as a single function of the sum of x?

[Gan_HOPE326]

I'm looking for a way to change a finite sum of square cosines:

$$\Sigma^{N}_{s=1}cos^{2}(x_{s})$$

into a single function of the sum of x:

$$f(\Sigma^{N}_{s=1}x_{s})$$

Is there a known way to do this, even if with an approximate method (i.e. Taylor series or such)?. It's ok if it just works in a $$\pi$$ range.

 

[hamster143]

Can't be done. If $N=2, x_1=0, x_2=\pi$, sum of x is $\pi$ and sum of cosines is 2. IF $N=2, x_1=\pi/2, x_2=\pi/2$, sum of x is still $\pi$, but sum of cosines is 0.