if cos a + cos b = c, sin a + sin b= d and a-b = 2 theta, then cos 3 theta / cos theta is

Hello student, Please find the answer to your question below

cos a + cos b = c
sin a + sin b= d
a-b = 2 theta

use
CosC + CosD = 2Cos[(C+D)/2]Cos[(C-D)/2]
SinC + SinD = 2Sin[(C+D)/2]Cos[(C-D)/2]

dividing we get c / d = cot (a+b)/2
cos 3 theta / cos theta = 4 cos ^2 theta – 3