To Show that $(e^{B_t^1}cos(B_t^2))_{t \in \mathbb{R_+}}$ (where: $B=(B_s^1,B_s^2)$ is a 2-dimensional Brownian Motion) is a Martingal I used Ito's Lemma and showed that this is equal to: $ 1+ \int_0^t{e^{B_s^1}cos(B_s^2)dB_s^1}-\int_0^t{e^{B_s^1}sin(B_s^2)dB_s^2}$.
How do I show that this is a Martingale?
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