If α + β - γ = π, and sin2 α + sin2 β – sin2 γ = λ sin α sin β cos γ, then write the value of λ.
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)