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Question

If cosA=sinB2sinC, then in ΔABC

A
c=a
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B
b=c
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C
cosB=cos2C
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D
sinB=sin2C
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Solution

The correct options are
A c=a
D sinB=sin2C
cosA=sinB2sinC

using cosine rule and sine rule

b2+c2a22bc=b2c
b2+c2a2=b2
c2=a2
c=a
Hence sinC=sinA
cosA=sinB2sinC
2sinC.cosA=sinB.
Now
sinC=sinA
Hence,
sin2A=sinB.
sin2C=sinB.

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