Trigonometric Function

The expression $f(x)=\sqrt{8-8\cos{x}}+\sqrt{8+8\cos{x}}$ can be rewritten as $f(x)=4\sin{0.5x}+4\cos{0.5x}=4\sqrt{2}(\sin{(0.5x+0.25π)})$ using the Half Angle identities and the R-Method. Since the Domain is $[0,π]$ , $\sin{0.5x}$ and $\cos{0.5x}$ are both positive so the minimum value of $\sin{(0.5x+0.25π)}$ is $0.5\sqrt{2}$ when $x=0$ and maximum at $1$ when $x=0.5π$ . Thus, $4\sqrt{2}*(1+0.5\sqrt{2})$ is approximately $9.65685$ , which is the final answer.