1/(sinα-1)-1/(sinα+1)=(sinα+1-sinα+1)/((sinα-1)(sinα+1))=
=2/(sin²α-1)=-2/(1-sin²α)=-2/cos²α=-2*sec²α.
1/(sinα-1)-1/(sinα+1)=(sinα+1-sinα+1)/((sinα-1)(sinα+1))=
=2/(sin²α-1)=-2/(1-sin²α)=-2/cos²α=-2*sec²α.