Question

verify the identity:

1-cos^2x/1-sinx= -sinx

Answer 1

assume you mean (this took some serious detective work - please be careful with parentheses)

1- (cos^2x)/(1-sinx)= -sinx
cos^2x = 1 - sin^2 x
so we have
1 - (1-sin x)(1+sin x)/(1-sin x) = -sin x

1 - (1+sin x) = -sin x

1 - 1 - sin x = -sin x

-sin x = -sin x