Question

sinA+sinB/cosA+cosB=tan(A+B/2)​

Answer 1

Answer:

Use formulas

$\sin(x) + \sin(y) = 2 \sin( \frac{x + y}{2} ) \cos( \frac{x - y}{2} ) \\ \cos(x) + \cos(y) = 2 \cos( \frac{x + y}{2} ) \cos( \frac{x - y}{2} )$

As you can see cos terms cancels out and you get desired result.