Use Theorem s(x+y)= s(x)c(y)+c(x)s(y) to show
cos(4x)=
Then apply this formula to find the value of cos(/8)
$\displaystyle \cos(4x)=\cos(2(2x))=1-2\sin^2(2x)=1-2(\sin(x+x))^2$
Now apply the angle-sum identity for sine as required.
Then use:
$\displaystyle x=\frac{\pi}{8}$ in the resulting formula. I would suggest letting $\displaystyle u=\cos^2(x)$ to get a quadratic in $\displaystyle u$. Take the appropriate root.