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Question

In a \triangle ABC, if b2+c2=3a2, then cot B + cot C = cot A =

A
1
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B
ab4
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C
\N
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D
ac4
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Solution

The correct option is C \N
cot B+cot Ccot A=cos Bsin B+cos Csin Ccot A
=sin C cos B+cos C sin Bsin B sin Ccos A=sin(B+C)sinB sinCcos Asin A
=sin2 Asin B sin C cos Asin A sin B sin C=a2bc cos Ak(abc)
Since=sinAa=sinBb=sinCc = k (say)
and cos A=b2+c2a22bc=a2bc(b2+c2a2)2bc(abc)k
(a2a2)abc K=0,{Asb2+c2a22=3a2a22=2a22=a2.}

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