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Question

In triangle ABC,a2+c2=2002b2, then cotA + cotCcotB is equal to


A

12001

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B

22001

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C

32001

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D

42001

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Solution

The correct option is B

22001


cotA + cotCcotB=cosAsinA + cosCsinCcosBsinB=sin(A+C)sinBsinAcosBsinC=sin2BsinAcosBsinC=4R2b24R2accosB=2b22accosB=2b2a2+c2b2=2b22002b2b2=22001


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