Given sin (2a + b) = 2sinb, prove Tan (a + b) = 3tana

Given sin (2a + b) = 2sinb, prove Tan (a + b) = 3tana

sin(2a+B)=2sinB
sin[(a+B)+a]=2sin[(a+B)-a]
sin(a+B)cosa+cos(a+B)sina=2sin(a+B)cosa-2cos(a+B)sina
sin(a+B)cosa=3cos(a+B)sina
Divide both sides by cos (a + b) cosa
Then Tan (a + b) = 3tana