if cosx + cosy=4/5 and cosx - cosy=2/7 prove that 14tan(x-y/2)+5cot(x+y/2)=0

adding both you get cosx subtracting cosy so we also got sinx and siny if we use half angle formulas we can write sinx in terms of tanx/2 so we got that too so we can solve

This question solve using half angle formulas we can write sinx in terms of tanx/2 so we got that then solve this problem.