Question

if tan(a+b)=3tana prove sin(2a+b)=2sinb

Answer 1

refer to the image attached for solution

Answer 2

Answer:

Step-by-step explanation:

tan (a + b ) = 3 tan a

= tan (a + b) = 3/1

Using Componendo and Dividendo rule

= tan (a + b) + tan a / tan (a + b) - tan a = 3 + 1 / 3 - 1

= Sin (a + b + a) /cos (a + b). Cos a /sin (a+b-a) / cos (a+b).cos a = 4/2

= Sin(2a + b)/sin b = 2

= Sin (2a + b) = 2 sinb

                      Proved