How can we compute the sum $$ \sin(f_1) + \sin(f_2) $$ I know it is $$ 2\sin\left(\frac{f_2 + f_1}{2}\right) \cos\left(\frac{f_2 - f_1}{2}\right) $$ but how can it be derived with elementary trigonometric identites?
Sum of two sine curves
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trigonometry