Question 535932
(1)
LHS =[sinx sec^2x + sinx - 2tanx] / (cosx - 1)^2    (tanx=sinx/cosx=secx/cosecx)
    =[sinx(sec^2x + 1- 2secx)]/[(1/secx-1]^2
    =[sinx(sec^2x + 1- 2secx)] / [(1-secx)/secx]^2   
    =[sinx(sec^2x + 1- 2secx)] / [(1-2secx+ sec^2x)/sec^2x]  
    =[sinx(sec^2x + 1- 2secx)]*[(sec^x2)/(1-2secx+ sec^2x)]
    =sinx*sec^2x  [cancelling out (sec^2x + 1- 2secx)]
    =sinx*1/cosx*secx   (tanx=sinx/cosx=secx/cosecx)
    =tanx*secx=secx*tanx=RHS

(2)
LHS =[sin^3(x)-cos^3(x)] /[sin(x) - cos(x)]
    =[(sinx-cosx)(sin^2x+sinxcosx+cos^2x)] / (sinx-cosx)
    =sin^2+sinxcosx+cos^2x {cancelling out (sinx-cosx)]
    =1+sinxcosx  (using identity sin^2+cos^2x=1)
    =RHS