Question 313671
Define everything by its definition. secx=1/cosx, cscx = 1/sinx, and tanx =sinx/cosx


(sinx)(secx-cscx)-tanx= -1
(sinx)(1/cosx - 1/sinx) -sinx/cosx = -1
sinx/cosx -sinx/sinx -sinx/cosx = -1
sinx/cosx -1 -sinx/cosx = -1


Note: sinx/cosx -sinx/cosx =0


Therefore,

-1 = -1