Question

cosx+sinx ÷cosx-sinx=​

Answer 1

Answer:

$= \frac{ \cos(x) + \sin(x) }{ \cos(x) - \sin(x) } = \frac{( \cos(x) + \sin(x) )( \cos(x) + \sin(x) ) }{( \cos(x) - \sin(x) )( \cos(x) + \sin(x) )} \\ = \frac{ { \cos^{2}(x) + { \sin^{2}(x) } + 2 \sin(x) \cos(x) } }{ \cos^{2}(x) - \sin^{2}(x) } \\ = \frac{1 + \sin(2x) }{ \cos(2x) } = \frac{1}{ \cos(2x) } + \frac{ \sin(2x) }{ \cos(2x) } \\ = \sec(2x) + \tan(2x)$