You can put this solution on YOUR website! verify by changing the left side only:
sinX/1-cotX - cosx/tanX-1 = sinX + cosX
**
(sin/1-cot)-(cos/tan-1)
[sin/(1-cos/sin)]-[cos/(sin/cos-1)]
[sin/(sin-cos)/sin)]-[cos/(sin-cos)/cos]
[sin^2/(sin-cos)]-[cos^2/(sin-cos)]
(sin^2-cos^2)/(sin-cos)
(sin+cos)(sin-cos)/(sin-cos)
sinx+cosx