Let $(B_t)_{t \ge 0 }$ be a standard Brownian Motion and let $(X_t)_{t \ge 0}$ be defined by $$X_t= e^{-t/2}cosh(B_t).$$
For each $s\le t$, calculate the covariance between $X_s$ and $X_t$.
Before getting to this question I showed that $(X_t)_{t \ge 0}$ is a martingale. So, $E[X_s]E[X_t]=1$, right?