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Solving Simultaneous Trigonometric Equations

If α +β -γ ...

Question

If $α + β - γ = π$ , show that ${sin}^{2} α + {sin}^{2} β - {sin}^{2} γ = 2 sin α sin β cos γ$ .

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α + β - γ = π,

{sin}^{2} α + {sin}^{2} β - {sin}^{2} γ = 2 sin α sin β cos γ

α + β + γ = π

{sin}^{2} α + {sin}^{2} β - {sin}^{2} γ

α + β - γ = π,

{sin}^{2} α + {sin}^{2} β - {sin}^{2} γ = m sin α sin β cos γ

sin 2 (α - β) + sin 2 (β - γ) + sin 2 (γ - α)

= - 4 sin (α - β) sin (β - γ) sin (γ - α)

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