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Question

In a ABC, if cosAcosBcosC=318 and sinAsinBsinC=3+38, then

The value of tanAtanB+tanBtanC+tanCtanA is

A
543
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B
5+43
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C
6+3
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D
63
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Solution

The correct option is B 5+43
cos(A+B+C)=cosAcosBcosC[1tanAtanBtanBtanCtanCtanA]1=318×[1tanAtanBtanBtanCtanCtanA]1tanAtanBtanBtanCtanCtanA =813tanAtanB+tanBtanC+tanCtanA =1813=7313 =7+331×3+13+1=5+43

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