Question

If 2sin(A+B)=sinA+sinB prove that tan(A/2)tan(B/2)=1/3

Answer 1

Step-by-step explanation:

2sin(A)cos(B)+2sin(B)cos(A)=sin(A)+sin(B)

cos(B)=.5;      cos(A)=.5

A and B are both either pi/3 or -pi/3

Tan(pi/6)Tan(pi/6)=1/3

tan(pi/6)^2=1/3

Tan(pi/6)=1/$\sqrt{3}$

Proven

Answer 2

Step-by-step explanation:

1.extend sinA+sinB

2. extend sin(A+B)

THEN here you go .