Question

1+Ctg∝ +Csc∝) / 1+Tan∝ +Sec∝

Answer 1

$\frac{1+ctgx+cscx}{1+tanx+secx} =}\\\\{ \frac{1+\frac{cosx}{senx}+\frac{1}{sen}}{1+\frac{senx}{cosx}+\frac{1}{cosx}} =}\\\\{ \frac{ \frac{senx+cosx+1}{senx} }{ \frac{cosx+senx+1}{cosx} }=}\\\\{ \frac{senx+cosx+1}{senx} \times \frac{cosx}{senx+cosx+1} =}\\\\{ \frac{cosx}{senx} =}\\\\{\boxed{ctgx}}\\\\{\mathbf{salu2.!!\ :)}}\\{\mathbf{Wellington}}$