RD Sharma - Mathematics

Book: RD Sharma - Mathematics

Chapter: 7. Values of Trigonometric Functions at Sum of Difference of Angles

Subject: - Class 11th

Q. No. 1 of Very Short Answer

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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


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)


Chapter Exercises

More Exercise Questions


If then write the value of