for the smallest positive values of x and y the equation 2(sinx+sin y)-2cos(x-y)=3

(a)sinx+y/2=1

(b)cos(x-y/2)=1/2

(c)number ofordered pairs (x,y)is2

(d) number of orderd pairs(x,y)is3

Hello Student,

2(sinx+sin y)-2cos(x-y)=3
use this formula
SinC + SinD = 2Sin[(C+D)/2]Cos[(C-D)/2]

2(Sin[(x+y)/2]Cos[(x-y)/2])-2[2cos²[(x-y)/2] – 1}=3
take cos common and then simplify it further