If cosC – cosD = y, then the value of y is

$-2 cos left(frac{mathrm{C}+mathrm{D}}{2} ight) cdot cos left(frac{mathrm{C}-mathrm{D}}{2} ight)$

$2 sin left(frac{mathrm{C}+mathrm{D}}{2} ight) cdot sin left(frac{mathrm{C}-mathrm{D}}{2} ight)$

$2 cos left(frac{mathrm{C}+mathrm{D}}{2} ight) cdot cos left(frac{mathrm{C}-mathrm{D}}{2} ight)$

$-2 sin left(frac{mathrm{C}+mathrm{D}}{2} ight) cdot sin left(frac{mathrm{C}-mathrm{D}}{2} ight)$

Answer : Option D

Explanation :

Here,

cosC – cosD = y

$Rightarrow y=cos mathrm{C}-cos mathrm{D}$

$Rightarrow y=-2 sin$

$left(frac{mathrm{C}+mathrm{D}}{2} ight) cdot sin left(frac{mathrm{C}-mathrm{D}}{2} ight)$

$quad[ecause$

It is the basic formula of $cos mathrm{C}-cos mathrm{D}]$