We know that, $$sin(x+y) = sinxcosy + cosxsiny$$ --------(i) and $$sin(x-y) = sinxcosy-cosxsiny$$ ------------(ii) Adding equations (i) and (ii), we get : $$sin(x+y) + sin(x-y) = 2sinxcosy$$ ------------(iii) Let $$x + y = C$$ and $$x - y = D$$ => $$x = frac{C+D}{2}$$ and $$y = frac{C-D}{2}$$ Substituting above values in equation (iii) => $$sinC + sinD = 2sin(frac{C+D}{2})cos(frac{C-D}{2})$$ => Ans - (B)
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