Prove that (sinA-cosA+1)/(sinA+cos-1)=1/(secA-tanA)

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Swati Datta

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LHS = (sinA-cosA+1)/(sinA+cos-1) = (1 + sinA) (1 - sinA)/cos A(1 - sinA) = 1 - sin2A/cos A(1 - sinA) = cos2A/cos A(1 - sinA) = cosA/(1 - sinA) = 1/ (1/cosA - sinA/cosA) = 1/(secA - tanA) = RHS Hence Proved
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LHS = (sinA-cosA+1)/(sinA+cos-1) = (1 + sinA) (1 - sinA)/cos A(1 - sinA) = 1 - sin2A/cos A(1 - sinA) = cos2A/cos A(1 - sinA) = cosA/(1 - sinA) = 1/ (1/cosA - sinA/cosA) = 1/(secA - tanA) = RHS Hence Proved
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divide Numerator and Denominator bu Cos A = Tan A - 1 + Sec A / Tan A + 1 - Sec A since (1+ Tan^2 A) = Sec^2 A or 1 = Sec^2 A - Tan^2 A =( Tan A + Sec A - 1) / =( Tan A + Sec A - 1) / = ( Tan A + Sec A - 1) / = ( Tan A + Sec A - 1) / = 1/ {sec A - Tan A}
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divide Numerator and Denominator bu Cos A = Tan A - 1 + Sec A / Tan A + 1 - Sec A since (1+ Tan^2 A) = Sec^2 A or 1 = Sec^2 A - Tan^2 A =( Tan A + Sec A - 1) / [Tan A - Sec A+( Sec^2 A - Tan^2 A)] =( Tan A + Sec A - 1) / [(Tan A - Sec A)+( Sec^2 A - Tan^2 A)] = ( Tan A + Sec A - 1) / [- ( Sec A - tan A) + ( Sec^2 A - Tan^2 A)] = ( Tan A + Sec A - 1) / [ ( Sec A - tan A){ Tan A + Sec A - 1] = 1/ {sec A - Tan A} read less
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LHS = (sinA-cosA+1)/(sinA+cos-1) = (1 + sinA) (1 - sinA)/cos A(1 - sinA) = 1 - sin2A/cos A(1 - sinA) = cos2A/cos A(1 - sinA) = cosA/(1 - sinA) = 1/ (1/cosA - sinA/cosA) = 1/(secA - tanA) = RHS
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LS= Sin A - CosA +1 / Sin A + Cos A -1 divide Numerator and Denominator by Cos A = Tan A - 1 + Sec A / Tan A + 1 - Sec A since (1+ Tan^2 A) = Sec^2 A or 1 = Sec^2 A - Tan^2 A =( Tan A + Sec A - 1) / =( Tan A + Sec A - 1) / = ( Tan A + Sec A - 1) / = ( Tan A + Sec A - 1) / = 1/ {sec...
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LS= Sin A - CosA +1 / Sin A + Cos A -1 divide Numerator and Denominator by Cos A = Tan A - 1 + Sec A / Tan A + 1 - Sec A since (1+ Tan^2 A) = Sec^2 A or 1 = Sec^2 A - Tan^2 A =( Tan A + Sec A - 1) / [Tan A - Sec A+( Sec^2 A - Tan^2 A)] =( Tan A + Sec A - 1) / [(Tan A - Sec A)+( Sec^2 A - Tan^2 A)] = ( Tan A + Sec A - 1) / [- ( Sec A - tan A) + ( Sec^2 A - Tan^2 A)] = ( Tan A + Sec A - 1) / [ ( Sec A - tan A){ Tan A + Sec A - 1] = 1/ {sec A - Tan A} = RS..proved read less
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LHS = (sinA-cosA+1)/(sinA+cos-1) = (1 + sinA) (1 - sinA)/cos A(1 - sinA) = 1 - sin2A/cos A(1 - sinA) = cos2A/cos A(1 - sinA) = cosA/(1 - sinA) = 1/ (1/cosA - sinA/cosA) 1/(secA-tanA)
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LHS = (sinA-cosA+1)/(sinA+cos-1) = (1 + sinA) (1 - sinA)/cos A(1 - sinA) = 1 - sin2A/cos A(1 - sinA) = cos2A/cos A(1 - sinA) = cosA/(1 - sinA) = 1/ (1/cosA - sinA/cosA) = 1/(secA - tanA) = RHS Hence Proved
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LHS = (sinA-cosA+1)/(sinA+cos-1) = (1 + sinA) (1 - sinA)/cos A(1 - sinA) = 1 - sin2A/cos A(1 - sinA) = cos2A/cos A(1 - sinA) = cosA/(1 - sinA) = 1/ (1/cosA - sinA/cosA) = 1/(secA - tanA) = RHS Hence Proved
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LHS=(sinA-cosA+1)/(sinA+cos-1) =(1+sinA) (1-sin A)/cosA(1-sinA) =1-sin2A/cos A(1-sinA) =cos2A/cos A(1-sinA) =cos A/(1-sin A) =1/(1/cosA-sin A/cos A) =1/(sec A-tan A) =RHS
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