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Question Number 48711 by somil last updated on 27/Nov/18

Commented by mr W last updated on 27/Nov/18

A+B+C=π  A+B=π−C  ((A+B)/2)=(π/2)−(C/2)  sin (((A+B)/2))=sin ((π/2)−(C/2))=cos (C/2)

$${A}+{B}+{C}=\pi \\ $$$${A}+{B}=\pi−{C} \\ $$$$\frac{{A}+{B}}{\mathrm{2}}=\frac{\pi}{\mathrm{2}}−\frac{{C}}{\mathrm{2}} \\ $$$$\mathrm{sin}\:\left(\frac{{A}+{B}}{\mathrm{2}}\right)=\mathrm{sin}\:\left(\frac{\pi}{\mathrm{2}}−\frac{{C}}{\mathrm{2}}\right)=\mathrm{cos}\:\frac{{C}}{\mathrm{2}} \\ $$

Answered by tanmay.chaudhury50@gmail.com last updated on 27/Nov/18

sin(((A+B)/2))  =sin(((π−C)/2))  =sin((π/2)−(C/2))  =Cos((C/2))

$${sin}\left(\frac{{A}+{B}}{\mathrm{2}}\right) \\ $$$$={sin}\left(\frac{\pi−{C}}{\mathrm{2}}\right) \\ $$$$={sin}\left(\frac{\pi}{\mathrm{2}}−\frac{{C}}{\mathrm{2}}\right) \\ $$$$={Cos}\left(\frac{{C}}{\mathrm{2}}\right) \\ $$

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