if cos x + cos y = 4/5, cosx – cos y = 2/7 then the value of 14 tan(x-y)/2 + 5 cot (x+y)/2 is

Hello student, Please find the answer to your question below

Use the following formulas to solve this questions
CosC + CosD = 2Cos[(C+D)/2]Cos[(C-D)/2]
CosC - CosD = 2Sin[(C+D)/2]Sin[(D-C)/2]

tan[(C+D)/2]tan[(C-D)/2]= 5 / 14
so14*tan[(C-D)/2]= 5* cot[(C+D)/2]

Now u can simplify:-

CosC + CosD = 2Cos[(C+D)/2]Cos[(C-D)/2] _1CosC - CosD = -2Sin[(C+D)/2]Sin[(C-D)/2]_2