Cos/1- tan + sin/1- cot = sin+cos...pls prove?

Question

Cos/1- tan + sin/1- cot = sin+cos...pls prove?

Answer 1

hi, could you please add on brackets? i.e. cos/(1- tan) + sin/(1- cot) = sin+cos

or however it's supposed to be?

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okay, I'm going to assume that the question is cos/(1- tan) + sin/(1- cot) = sin+cos and that it's standard sin/cos/tan theatas.

cos/(1-(sin/cos)*) + sin/(1-(cos/tan)**) = sin + cos

cos/(cos-sin)+ sin/(sin-cos) = sin + 1 - sin***

cos/(cos-sin) - sin/(cos - sin) = 1

(cos - sin)/(cos-sin) = 1

1=1

therefore, cos/(1- tan) + sin/(1- cot) = sin+cos

Answer 2

LS = (cosx)/(1-tanx)+(sinx)/(1-cotx)

          change tanx to sinx/cosx, cotx to cosx/sinx

     = (cosx)/(1-(sinx/cosx))+(sinx)/(1-(cosx/s...

      multiply the first term by cosx/cosx, 2nd term by sinx/sinx (really multiplying both terms by 1

     = ((cosx)(cosx))/(cosx-sinx)+((sinx)(sinx)...

      multiply the first term by -1/-1 to get a common denominator

     = -((cosx)(cosx))/(sinx-cosx)+((sinx)(sinx...

     add the fractions

     = (sin^2x-cos^2x)/(sinx-cosx)

      use difference of squares to factor the numerator

     = ((sinx+cosx)(sinx-cosx))/(sinx-cosx)

       sinx-cosx in the numerator cancels with sinx-cosx in the denominator

     =sinx+cosx!