sin 2A + sin 2B – sin 2C 

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

Using formula, sin (A + B) = sin A cos B + cos A sin B 

= sin 2A + sin 2B - sin 2C 

Using formula 

sin2A = 2sinAcosA 

= 2sinAcosA + 2sinBcosB - 2sinCcosC 

Since A + B + C = π 

→ B + C = 180 - A

And sin(π – A) = sinA 

= 2sin(B + C)cos A + 2sin(A + C)cosB - 2sin(A + B)cosC 

= 2 ( sin B cos C + cos B sin C ) cos A + 2(sinAcosC + cosAsinC)cosB - 2(sinAcosB + cosAsinB )cosC 

= 2cosAsinBcosC + 2cosAcosBsinC + 2sinAcosBcosC + 2cosAcosBsinC– 2sinAcosBcosC – 2cosAsinBcosC 

= 2cosAcosBsinC + 2cosAcosBsinC 

= 4cosAcosBsinC 

= R.H.S