Question

___cosb=1/2[sin(a+b) + sin(a-b)

Answer 1

Use the addition and subtraction theorem:

sin (A + B) = sin A + cos B
sin (A - B) = sin A - cos B

From there it's just a matter of simplification.

sin A cos B = 1/2 [ sin (A + B) + sin (A - B) ]
sin A cos B = 1/2 [ sin A cos B + cos A sin B + sin (A - B) ]
sin A cos B = 1/2 [ sin A cos B + cos A sin B + sin A cos B - cos A sin B ]
sin A cos B = 1/2 [ 2 sin A cos B ]
sin A cos B = sin A cos B