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If A+B+C=pi, prove that : (cosA)/(sinb s...

If `A+B+C=pi`, prove that : `(cosA)/(sinb sinC) + (cosB)/(sinC sin) + (cosC)/(sinA sinB) =2`.

Text Solution

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`(CosA)/(sinBsinC)+(CosB)/(sinC sinA)+(cosC)/(sinAsinB)`
`=(-cos(B+C))/(sinB sinC)+(-cos(A+C))/(sinC sinA)+(-cos(A+B))/(sinA sinB)`
`=-[cotB cotC+cot AcotC+cotAcotB-3]`
`=-[cotBcotC+cotAcotC+cotAcotB-3]`
`=-[1-3]=2`
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