alleryStart learning →A sum of sines, sinC + sinD, factorises as
A2 cos((C+D)/2) sin((C−D)/2)
B2 cos((C+D)/2) cos((C−D)/2)
C2 sin((C+D)/2) cos((C−D)/2)
D2 sin((C+D)/2) sin((C−D)/2)
Answer & Solution
Correct answer: C. 2 sin((C+D)/2) cos((C−D)/2)
Setting C = A + B and D = A − B in the product to sum rule gives sinC + sinD = 2 sin((C+D)/2) cos((C−D)/2).
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