Question

Prove that dy/dx of cosx+sinx/cosx-sinx = sec^2 pi/4+x

Answer 1

$y = \frac{ \cos(x) + \sin(x) }{ \cos(x) - \sin(x) } \ \\ \frac{dy}{dx} = \frac{ \cos(x) - \sin(x) ( - \sin(x) + \cos(x)) - \cos(x) + \sin(x) ( - \sin(x) - \cos(x) }{ { \cos(x) - \sin(x) }^{2} } \\ \frac{dy}{dx} = \frac{ - \sin(x) \cos(x) + \sin( ^{2} )x + \cos( ^{2} ) x - \sin(x) \cos(x) + \sin(x) \cos(x) + \sin ^{2} (x) + \cos ^{2} (x) + \sin(x) \cos(x) }{ { \cos(x) - \sin(x) }^{2} } \\ 2 \sec(2x)$
hey mate here is your answer!!!