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In a triangle A B C , if cos A=(sinB)/(2...

In a triangle `A B C` , if `cos A=(sinB)/(2sinC)` , show that the triangle is isosceles.

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`cos A = sinB/(2sinC)`
`=>sinB = 2sinCcosA`
As, `A+B+C = pi =>B = pi-(A+C)`
`=>sin(pi-(A+C)) = 2sinCcosA`
`=>sin(A+C) = 2sinCcosA`
`=>sinAcosC +cosAsinC = 2sinCcosA`
`=>sinAcosC -cosAsinC`
`=>sin(A-C) = 0`
...
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