Question

Question #92c75

Answer 1

`"The L.H.S.="cos^2x/(1-tanx)+sin^3x/(sinx-cosx),`

`=cos^2x/(1-sinx/cosx)+sin^3x/(sinx-cosx),`

`=cos^3x/(cosx-sinx)-sin^3x/(cosx-sinx),`

`=(cos^3x-sin^3x)/(cosx-sinx),`

`={cancel((cosx-sinx))(cos^2x+cosxsinx+sin^2x)}/cancel((cosx-sinx)),`

`=(cos^2x+sin^2x)+cosxsinx,`

`=1+sinxcosx,`

`"=The R.H.S."`

N.B.:- I have modified the Question so as to match with

the R.H.S.

The Problem can also be put in this way :

`"Prove : "cos^2x/(1-tanx)+sin^2x/(1-cotx)=1+sinxcosx.`

Enjoy Maths.!