Question

cosx + sinx /cosx-sinx differentiate the following​

Answer 1

$\frac{d}{dx}( \frac{cosx + sinx}{cosx - sinx} )\\ = \frac{(cosx - sinx) \frac{d}{dx} (cosx + sinx) - (cosx + sinx) \frac{d}{dx}(cosx - sinx) }{( {cosx - sinx})^{2} } \\ = \frac{(cosx - sinx)( - sinx + cosx) - (cosx + sinx)( - sinx - cosx)}{( {cosx - sinx})^{2} } \\ = \frac{( {cosx - sinx})^{2} + ( {cosx + sinx})^{2} }{( {cosx - sinx})^{2} } \\ = \frac{2}{( {cosx - sinx})^{2} }$