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 Question from Tehmas, a student: Prove sinC+sinD=2sin(C+D/2)cos(C-D/2)

Hi Tehmas,

Write the expression for $\sin(A + B).$

Write the expression for $\sin(A - B).$

Harley

Tehmas responded

I don't get it

$\sin (A + B) = \sin A \cos B + \cos A \sin B$
then use this to find an expression for $\sin (A - B) = \sin(A + (-B)).$ Add these expressions to obtain a formula for $\sin(A + B) + \sin(A - B).$