find $\theta(x),$ such that the minimum value of
$F=S\int_0^l \left\{\frac{1}{2} k[\frac{d\theta(x)}{dx}]^2-\frac{1}{2}E^2 \cdot \triangle \epsilon \cdot \cos^2 \theta (x)\right\}dx$
is achieved.
Actually I have the answer from my book, but no reasoning is stated there, could any one give me a hand?
Note that $E, \triangle \epsilon, k, S, l$ are constants here, indicating some physics parameters.
Sorry for having made a typo in the previous post, I've changed it from $cos \theta(x)$ to $cos^2 \theta(x).$