Help! Verify the Trigonometry Identity, Explain how to do

1 - (sin²x)/(1-cosx) = -cosx

Note that sin²(x) = 1 - cos²(x) = (1 - cos(x))(1 + cos(x)).

1 - sin²(x)/(1 - cos(x)) = 1 - (1 - cos(x))(1 + cos(x))/(1 - cos(x))

= 1 - (1 + cos(x)) = 1 - 1 - cos(x) = -cos(x).

1- (1-cosx^2)/1-cosx = 1- (1-cosx)(1+cosx) /(1-cosx) = -cosx