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  • Prove that: cosec A /(cosec A-1)+cosec A/(cosec A +1 )=2sec^2 A?

Prove that: cosec A /(cosec A-1)+cosec A/(cosec A +1 )=2sec^2 A?

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eginaligned & ext Given LHS:- fracoperatornamecosec Aoperatornamecosec heta+1+fracoperatornamecosec Aoperatornamecosec A-1\\ & ext Taking LCM \\ &fracoperatornamecosec Aoperatornamecosec A+1+fracoperatornamecosec Aoperatornamecosec A-1=fracoperatornamecosec^2 A-operatornamecosec A+operatornamecosec^2 A+operatornamecosec Aoperatornamecosec^2 A-1\\ &=frac2 operatornamecosec^2 Aoperatornamecosec^2 A-1\\ & (ecause operatornamecosec^2 A-1=cot ^2 A )\\ &=frac2 operatornamecosec^2 Acot ^2 A=fracfrac2sin ^2 Afraccos ^2 Asin ^2 A=2 sec ^2 A endaligned

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Deependra Verma

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