If sinA+sinB=1/2 and cosA+cosB=1/2 then the value of tanA+tanB

Answer 1

-2/3
proof:
1. observe symmetry in A and B
2. Square each equation after sending terms of A/B on other side. We can prove:
SinA + CosA= 1/2 and SinB +CosB=1/2

3. bring equations in form of tan's by dividing CosA and then using SecA to TanA formulae.

4. Solve the quadratic obtained and the sum of the solutions is the sum of TanA and TanB