Prove that the nonzero solutions to $x^{\prime \prime}+(1+\cos (t \sin (t))) x=0$ are oscillatory, that is $x(t)$ has infinitely many zeros.
I think that I have to use Sturm Picone's Comparison theorem but I am clueless about the function I have to compare with. Otherwise, I tried to think in terms of Pruffer angle but didn't get it.