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In a Delta A B C , if cosC=(sinA)/(2sinB...

In a `Delta A B C` , if `cosC=(sinA)/(2sinB)` , prove that the triangle is isosceles.

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Given,
`cosC=sinA/(2sinB)`
Let A,B,C be three sides of traingle ABC,So by given,
`=>2sinBcosC=sinA...(i)`
as `2sinBcosC=sin(B+C)+sin(B-C) `so equation (i) becomes,
`=>sin(B+C)+sin(B-C)=sinA`
`=>sin(180-A)+sin(B-C)=sinA`
`=>sinA+sin(B-C)=sinA`
...
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