Question

simplify the following:

cosx/1+sinx + 1+sinx/cosx

Answer 1

\[\frac{cosx}{1+sinx} + \frac{1+sinx}{cosx}\]\[=\frac{cosx}{1+sinx}\times \frac{1-sinx}{1-sinx} + \frac{1+sinx}{cosx}\]\[=\frac{cosx(1-sinx)}{(1+sinx)(1-sinx)} + \frac{1+sinx}{cosx}\]\[=\frac{cosx(1-sinx)}{1-sin^2x} + \frac{1+sinx}{cosx}\]\[=\frac{cosx(1-sinx)}{cos^2x} + \frac{1+sinx}{cosx}\]\[=\frac{cosx(1-sinx)}{cos^2x} + \frac{(cosx)(1+sinx)}{cos^2x}\]\[=\frac{cosx(1-sinx)+(cosx)(1+sinx)}{cos^2x}\]\[=...\]