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Question

In a ΔABC, angles A,B,C are in A.P. then limAC34sinAsinC|AC| is

A
1
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B
2
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C
3
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D
4
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Solution

The correct option is A 1
A,B,C are in A.P. B=60
cosB=cos60=12=c2+a2b22caa2+c2=b2+ac(ac)2=b2ac|ac|=b2ac|sinAsinC|=sin2BsinAsinC2cosA+C2sinAC2=34sinAsinC.2sinAC2=34sinAsinCso that limAC34sinAsinC|AC|=limAC2sinAC2|AC|=1

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