If A+B+C=180° and CosA=CosB×CosC,prove that:TanA=TanB+TanC
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[tex] Tan b + Tan c = \frac{Sinb cos c + cos bsin c}{cosacosb} =
\frac{sin(a+b)}{cos a}[/tex]
[tex] b + c = 180 -a =) sin(b + c) = sin( 180 -a) = sin a Plugging this result in the previous equation we get {sina}/{cos a} = Tan a QED[/tex]
[tex] b + c = 180 -a =) sin(b + c) = sin( 180 -a) = sin a Plugging this result in the previous equation we get {sina}/{cos a} = Tan a QED[/tex]
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