(sinx+1-cos^2x)/(cos^2x)=(sinx)/(1- sinx) need verifying the identity

We have (sinx+1)/(cos^2x) - (cos^2x)/(cos^2x) = (sinx - 1 + 1)/(1-sinx);
Then, (sinx+1)/(cos^2x) - 1 = (sinx - 1)/(1 - sinx) + 1/( 1 - sinx );
 (sinx+1)/(cos^2x) - 1 = -1 + 1/( 1 - sinx );
 (sinx+1)/(cos^2x) = 1/( 1 - sinx );
Finally, (1+sinx)(1-sinx) = cos^2x;
1 - sin^x = cos^2x;
cos^x = cos^2x; 
The identity is false!