\( \definecolor{colordef}{RGB}{249,49,84} \definecolor{colorprop}{RGB}{18,102,241} \)
  1. Show that \(\sin(A + B) + \sin(A - B) = 2 \sin A \cos B\).
  2. Hence show that \(\sin A \cos B = \frac{1}{2} \sin(A + B) + \frac{1}{2} \sin(A - B)\).
  3. Hence write the following as sums:
    1. \(\sin 30^\circ \cos \theta\)
    2. \(\sin 6\alpha \cos \alpha\)

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