## 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

Listen NCERT Audio Books to boost your productivity and retention power by 2X.

1
##### 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)

1
2
3
4
5
6
7
8
9
10
11
12