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Question Number 86614 by mathocean1 last updated on 29/Mar/20

ABC is an isocel triangle such as  AB=AC=3  and BC=4  α , β , and γ are its angles.  Show that cos(((α+β)/2))=sin((γ/2))  Hi sirs...

$${ABC}\:{is}\:{an}\:{isocel}\:{triangle}\:{such}\:{as} \\ $$$${AB}={AC}=\mathrm{3}\:\:{and}\:{BC}=\mathrm{4} \\ $$$$\alpha\:,\:\beta\:,\:{and}\:\gamma\:{are}\:{its}\:{angles}. \\ $$$${Show}\:{that}\:{cos}\left(\frac{\alpha+\beta}{\mathrm{2}}\right)={sin}\left(\frac{\gamma}{\mathrm{2}}\right) \\ $$$${Hi}\:{sirs}... \\ $$

Answered by TANMAY PANACEA. last updated on 29/Mar/20

((α+β)/2)  =((π−γ)/2)  =(π/2)−(γ/2)  cos(((α+β)/2))  =cos((π/2)−(γ/2))  =sin(γ/2)

$$\frac{\alpha+\beta}{\mathrm{2}} \\ $$$$=\frac{\pi−\gamma}{\mathrm{2}} \\ $$$$=\frac{\pi}{\mathrm{2}}−\frac{\gamma}{\mathrm{2}} \\ $$$${cos}\left(\frac{\alpha+\beta}{\mathrm{2}}\right) \\ $$$$={cos}\left(\frac{\pi}{\mathrm{2}}−\frac{\gamma}{\mathrm{2}}\right) \\ $$$$={sin}\frac{\gamma}{\mathrm{2}} \\ $$$$ \\ $$

Commented by mathocean1 last updated on 29/Mar/20

thank you sir.

$${thank}\:{you}\:{sir}. \\ $$

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