using the product formulas?

Question

Write the product as a sum: sin 50 cos 30

Answer 1

sin (A + B) = sin A cos B + cos A sin B
sin (A - B) = sin A cos B - cos A sin B
sin (A + B) + sin (A - B) = 2 sin A cos B
(1/2) [sin (A + B) + sin (A - B) ] = sin A cos B
(1/2) [ sin 80° + sin 20°] = sin 50° cos 30°

Answer 2

Write the product as a sum:
sin 50 cos 30

sinx cosy = (1/2){ sin(x-y) +sin(x+y)}

x =50
y =30

sin 50 cos 30 = (1/2){ sin(20) +sin(80)}

Answer 3

sin 50 cos 30
= (1/2)sin(50+30) + (1/2)sin(50-30)
= (1/2)sin 80 + (1/2)sin 20
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Ideas:
sin(a+b) + sin(a-b) = 2sin a sin b