2cos[(C+D)/2].cos[(C-D)/2] is equal to

Expression : 2cos[(C+D)/2]cos[(C-D)/2]

Using the formula : $$cos x . cos y = \frac{1}{2} [cos (x + y) + cos (x - y)]$$ --------------(i)

Substituting $$(x + y) = C$$ and $$(x - y) = D$$

=> $$x = \frac{C + D}{2}$$ and $$y = \frac{C - D}{2}$$ in equation (i),

=> $$cos (\frac{C + D}{2}) . cos (\frac{C - D}{2}) = \frac{1}{2} [cos C + cos D]$$

=> $$2 . cos (\frac{C + D}{2}) . cos (\frac{C - D}{2}) = cos C + cos D$$

=> Ans - (C)