Question-158313

Question Number 158313 by mnjuly1970 last updated on 02/Nov/21

Answered by mr W last updated on 02/Nov/21

α,β,γ are angles of a triangle. F=((sin α cos α+sin β cos β+sin γ cos γ)/(sin α sin β sin γ)) F=((sin 2α+sin 2β+sin 2γ)/(2 sin α sin β sin γ)) F=((4 sin α sin β sin γ)/(2 sin α sin β sin γ)) F=2

$$\alpha,\beta,\gamma\:{are}\:{angles}\:{of}\:{a}\:{triangle}. \\ $$$${F}=\frac{\mathrm{sin}\:\alpha\:\mathrm{cos}\:\alpha+\mathrm{sin}\:\beta\:\mathrm{cos}\:\beta+\mathrm{sin}\:\gamma\:\mathrm{cos}\:\gamma}{\mathrm{sin}\:\alpha\:\mathrm{sin}\:\beta\:\mathrm{sin}\:\gamma} \\ $$$${F}=\frac{\mathrm{sin}\:\mathrm{2}\alpha+\mathrm{sin}\:\mathrm{2}\beta+\mathrm{sin}\:\mathrm{2}\gamma}{\mathrm{2}\:\mathrm{sin}\:\alpha\:\mathrm{sin}\:\beta\:\mathrm{sin}\:\gamma} \\ $$$${F}=\frac{\mathrm{4}\:\mathrm{sin}\:\alpha\:\mathrm{sin}\:\beta\:\mathrm{sin}\:\gamma}{\mathrm{2}\:\mathrm{sin}\:\alpha\:\mathrm{sin}\:\beta\:\mathrm{sin}\:\gamma} \\ $$$${F}=\mathrm{2} \\ $$

Commented by mnjuly1970 last updated on 02/Nov/21

$${thx}\:{mr}\:\:\:\mathcal{W} \\ $$

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