If ABC.be triangle then acosBcosC+bcosCcosA+ccosAcosB=abc/4R^2 prove it
If ABC.be triangle then acosBcosC+bcosCcosA+ccosAcosB=abc/4R^2 prove it
Soumen dey , 7 Years ago
Grade 12th pass
Trigonometry> If ABC.be triangle then acosBcosC+bcosCco...
1 AnswersAditya Varshney
=cosAcosBcosC[a/cosA + b/cosB + c/cosC]
using Sine rule:
=cosAcosBcosC(2R)[tanA + tanB + tanC]
{R= circumradius }
{tanA + tanB + tanC = tanAtanBtanC}
{tanA + tanB + tanC = tanAtanBtanC}
=cosAcosBcosC(2R)sinAsinBsinC/cosAcosBcosC
=2RsinAsinBsinC
again using the sine rule
= 2Rabc/2R*2R*2R
= abc/4R2
where a,b,c = sides of triangle
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