Q. 14.0( 4 Votes )

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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)

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