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Question

If in a ABC,cosA=sinB2sinC, prove that it is an isosceles triangle.

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Solution

We are given that 2cosAcosC=sinB
or sin(A+C)sin(AC)=sinB....(1)
But in a ,A+C=180oB so that
sin(A+C)=sinB
sin(AC)=0 (by (1))
AC=0 or A=C
Hence the triangle is isosceles

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