Not sure but for $X_t=sin(B_t)$ if I want to find $E(X_t|F_s)$ s<t where $F_s$ is information/ filtration s. I know that if the process is something like $x^{4}−6tx^{2}$ I should be separating this out into $E[B_t^{4}|F_s]-6tE[B_t^{2}|F_s]$ and so on. But I'm having the trouble with the intuition of how to go about this with trig functions
2026-04-23 19:12:29.1776971549
Conditional Expectation Brownian-Motion
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Hint: $X_t=\sin (B_t-B_s+B_s)=\sin (B_t-B_s) \cos B_s+\cos (B_t-B_s) \sin B_s$