# Quadratic Variation of Function of Brownian Motion

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.

• Can you compute its expectation and variance? (I'm not very familiar with the topic, it just seems like a natural thing to do.) – Dap Oct 3 '17 at 9:24
• thanks, as it turns out I think this is actually as far as the quadratic variation can be reduced – Flintro Oct 4 '17 at 13:06