# How do you prove [cosx/(1-sinx)] + [(1-sinx)/cosx]=2secx?

Apr 16, 2015

Just add like ordinary fractions. LCD is (1-sinx)cosx. The sum would be $\frac{{\cos}^{2} x + 1 - 2 \sin x + {\sin}^{2} x}{\left(1 - \sin x\right) \cos x}$

=$\frac{2 - 2 S \in x}{\left(1 - \sin x\right) \cos x}$

=$\frac{2}{\cos} x$

=2secx