Use the angle sum formulas to derive…

Question:

Use the angle sum formulas to derive sin (A – B) = sin A cos B – cos A sin B.

Answer:

Use the angle sum formulas

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

Substitute -B for B to obtain

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

Using sin ( -B) =-sinB and cos( -B) =cosB

sin (A – B) = sin A cos B – cos A sin B

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