If cos A + cos B = 1/2 and sin A + sin B = 1/4, prove that tan(A + B)/2 = 1/2

Question

If cos A + cos B = \(\frac{1}{2}\) and sin A + sin B = \(\frac{1}{4}\), prove that tan(\(\frac{A+B}{2}\)) = \(\frac{1}{2}\)

Answer 1

Given that cos A + cos B = \(\frac{1}{2}\) 

2 cos(\(\frac{A+B}{2}\)) cos(\(\frac{A-B}{2}\)) = \(\frac{1}{2}\)... (1)   

Also given that sin A + sin B = \(\frac{1}{4}\) ... (2) 

\(\frac{(2)}{(1)}\)gives