If - - - - - - - Find m if sin2 - - sin2 - - sin2 - - m sin - sin - cos -

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Trigonometric Ratios for Sum of Two Angles

If α + β - ...

Question

If $α + β - γ = π,$ Find m if ${sin}^{2} α + {sin}^{2} β - {sin}^{2} γ = m sin α sin β cos γ$

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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

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

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

\frac{t a n (α + β - γ)}{t a n (α - β + γ)} = \frac{t a n γ}{t a n β}

s i n (β - γ) = 0

s i n 2 α + s i n 2 β + s i n 2 γ = 0

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