Sin a + sin b : tolong dijawab

Identitas Trigonometri.

α + β = a
α - β = b
————- +
2α = a + b → α = 1/2 (a + b)

α + β = a
α - β = b
————- –
2β = a – b → β = 1/2 (a – b)

sin (α + β) + sin (α - β) = 2 sin α cos β
sin [1/2 (a + b) + 1/2 (a – b)] + sin [1/2 (a + b) – 1/2 (a – b)] = 2 sin [1/2 (a + b)] cos [1/2 (a – b)]
sin (1/2 a + 1/2 b + 1/2 a – 1/2 b) + sin (1/2 a + 1/2 b – 1/2 a + 1/2 b) = 2 sin [1/2 (a + b)] cos [1/2 (a – b)]
sin a + sin b = 2 sin [(a + b) / 2] cos [(a + b) / 2]