I am trying to compute the quadratic variation of $ \cos (B_t)$. Using Ito's formula I have deduced that we would get that the quadratic variation is given by: $$[\cos B](t) = \int^t_0 \sin^2(B_s)ds $$ but I can't reduce this problem any further as I can't compute this integral. Indeed I'm not even sure this is the right approach. Any hints would be welcome.
Thanks for the help.