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Question

In ABC, if cos A + cos C = 4 sin212B, then a, b, c are in

A

A. P.

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B

G. P.

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C
H. P.
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D
None of these
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Solution

The correct option is A

A. P.


cos A + cos C = 4 sin212B
2 cosA+C2cosAC2=4 sin2B2
cosA+C2cosAC2=2 sin2B2
cos(AC2)=2sinB2
cosA2cosC2sinA2sinC2=2sin B2
s(sa)bcs(sc)ab+(sb(sc)bc(sa)(sb)ab
=2(sa)(sc)ac(sa)(sc)ac+sbb(sc)(sa)ac=2(sa)(sc)ac
Sb+sb2=2 a+c=2b a,b,careinA.P.

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