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If cosecA + cotA = p then prove that cosA = p2-1/p2+1 |
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Answer» Wah ??? cosec A + cot A = p\xa0Squaring both Sides, we get\xa0{tex}(Cosec A+ cot A)^2 = p ^2{/tex}{tex}Cosec^2 A+ Cot^2A + 2 cosec A Cot A = p^2{/tex}{tex}1+ cot^2A + Cot^2A+2 CosecACotA = p^2{/tex}\xa0(using identity\xa0{tex}Cosec^2A = 1+ Cot^2A{/tex}){tex}1+2 Cot^2A+2CosecA CotA = p^2{/tex}{tex}2 Cot^2A+2 CosecACotA = p^2-1{/tex}2 Cot A(CotA+ Cosec A) =\xa0{tex}p^2-1{/tex}2p cot A=\xa0{tex}p^2-1{/tex}\xa0as cot A+ cosec A= p givenAgain\xa0{tex}p^2 = Cosec^2A+Cot^2A+2 CosecA CotA{/tex}Adding 1 to both sides , we get\xa0{tex}p^2+1 = Cosec^2A+ Cot^2A+2CosecA CotA +1{/tex}{tex}p^2+1 = Cosec^2A+Cosec^2A+2CosecACotA{/tex}(using identity\xa0{tex}1+ Cot^2A = Cosec^2A{/tex}){tex}p^2+1= 2 Cosec^2A+2 CosecACotA{/tex}{tex}p^2+1 = 2 CosecA(CosecA+ Cot A){/tex}{tex}p^2+1= 2p Cosec A{/tex}\xa0as CosecA+ Cot A= p given{tex}p^2-1/p^2+1= 2pCotA/2pCosecA{/tex}{tex}p^2-1/p^2+1 = CotA/ CosecA{/tex}{tex}p^2-1/p^2+1= CosA/ Sin A . 1/Sin A{/tex}{tex}p^2-1/p^2+1 = Cos A{/tex}\xa0 |
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