Trigonometric integral $\int_0^{\frac{\pi}{\omega}}\sin(\omega t)\cos(n\omega t)\,dt$

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How can I get the value of this integral? $$\int_0^{\frac{\pi}{\omega}}\sin(\omega t)\cos(n\omega t)\,dt$$

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Hint:

$\sin p\cos q=\dfrac{\sin(p+q)+\sin(p-q)}{2}$