Math CentralQuandaries & Queries


Question from Tehmas, a student:

Prove sinC+sinD=2sin(C+D/2)cos(C-D/2)

Hi Tehmas,

I can help you get started.

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

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

Add the two expressions.


Tehmas responded


I don't get it

Start with the expression

\[\sin (A + B) = \sin A \cos B + \cos A \sin B\]

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


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