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Porve that : (cosecA-sinA)(secA-cosA)`=(1)/(tanA+cotA)`

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L.H.S.`=("cosec"A-sinA)(secA-cosA)`
`=((1)/(sinA)-sinA/(1))((1)/(cosA)-(cosA)/(1))=((1-sin^(2)A)/(sinA))((1-cos^(2)A)/(cosA))`
`=((cos^(2)A)/(sinA))((sin^(2)A)/(cosA))=cosA sinA`
andR.H.S.`=(1)/(tanA+cotA)=(1)/(sinA/(cosA)+cosA/sinA)`
`=(1)/((sin^(2)A+cos^(2)A)/(sinAcosA))=(sinAcosA)/(1)=sinAcosA`
`:.` L.H.S.=R.H.S.

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