If tan - - tan - - tan -1 - tan - tan - Prove that- sin 2- - sin 2- - sin 2-1 - sin 2- sin 2-

tan β #160; = sin (α #160; + γ )cos (α #160; γ ) #160;on changing to sin and cos #160; ∴ #160; sin 2β #160; = 2 ta ...

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Relation between Roots and Coefficients for Quadratic

If tan β = ...

Question

If tan $β = \frac{tan α + tan γ}{1 + tan α tan γ},$ Prove that: $sin 2 β = \frac{sin 2 α + sin 2 γ}{1 + sin 2 α sin 2 γ}$

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tan β = \frac{tan α + tan γ}{1 + tan α tan γ}

sin 2 β = \frac{sin 2 α + sin 2 γ}{1 + sin 2 α sin 2 γ} .

\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

tan (α + β) + tan (α - β) = \frac{sin 2 α}{1 - {sin}^{2} α - {sin}^{2} β}

tan β = \frac{tan α + tan β}{1 + tan α tan β}

sin c β = \frac{sin 2 α + sin 2 γ}{1 + sin 2 α sin 2 γ}

c

α + β - γ = π

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

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