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prove that ((1-tanA)/(1-cotA))^2=tan^2A...

prove that `((1-tanA)/(1-cotA))^2=tan^2A`

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First term `=(1+tan^(2)A)/(1+cot^(2)A)=(sec^(2)A)/(cosec^(2)A)=(1/(cos^(2)A))/(1/(sin^(2)A))=(sin^(2)A)/(cos^(2)A)=tan^(2)A=`Third term
Again , second term `=((1-tanA)/(1-cotA))^(2) = ((1/(1)-sinA/cosA)^(2))/((1/(1)-cosA/(sinA))^(2))=(((cosA-sinA)/cosA)^(2))/(((sinA-cosA)/(sinA))^(2))`
`=((cosA-sinA)^(2))/(cos^(2)A)xx(sin^(2)A)/((sinA-cosA)^(2))`
`=(sin^(2)A)/(cos^(2)A)xx((cosA-sinA)^(2))/((cosA-sinA)^(2))` `[:'(x-y)^(2)=(y-x)^(2)]`
`=tan^(2)Axx1=tan^(2)A=` Third term
`:.(1+tan^(2)A)/(1+cot^(2)A)=((1-tanA)/(1-cot A))^(2)=tan^(2)A`
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