- #1
nomadreid
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Homework Statement
To show that sin A + sin B = +2|sin ((A+B)/2)*cos((A-B)/2)| is easy. However, it is not clear how to remove the absolute value signs to give the valid identity sinA + sin B = 2(sin ((A+B)/2)*cos((A-B)/2)) without having to go through many cases.
Homework Equations
To prove the version with the absolute value is a straightforward application on the RHS of the half-angle identities and the angle addition/subtraction identities, whereupon one gets
+√(sinA+sinB)2.
The Attempt at a Solution
I started with making a table of the different cases, some of which are straightforward. But the number of cases that must be examined gets to quickly be rather large, so I figure that there is an easier way to go about it. All help would be appreciated.