Answer :

α + β = π + γ

Sin (α + β) =sin (π + γ)


Sin (α) cos (β) + sin (β) cos (α)=-sin(γ)


Take square both side


[sin(α)cos(β)+sin(β)cos(α)]2=sin2(γ)


sin2(α)cos2(β)+sin2(β)cos2(α)+2 Sin(α)cos(β)sin(β)cos(α)= sin2(γ)


sin 2(α)[1-sin2(β)]+sin2(β)[1-sin2(α)]+2 Sin(α)cos(β)sin(β)cos(α)= sin2(γ)


sin 2(α)-Sin2(α)sin2(β)+sin2(β)-sin2(β)sin2(α) -sin2(γ)=- 2Sin(α)cos(β)sin(β)cos(α)


sin 2(α)+sin2(β)-sin2(γ)=2Sin2(α)sin2(β)- 2Sin(α)cos(β)sin(β)cos(α)


sin 2(α)+sin2(β)-sin2(γ)=-2Sin(α)sin(β)[ cos(β) cos(α)- Sin(α)sin(β)]


sin 2(α)+sin2(β)-sin2(γ)=-2Sin(α)sin(β) cos(α+ β)


sin 2(α)+sin2(β)-sin2(γ)=2Sin(α)sin(β) sin(γ)


Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
caricature
view all courses