Answer:
[tex]\csc \left(x\right)=\frac{\csc \left(x\right)+\sec \left(x\right)}{1+\tan \left(x\right)}[/tex]
[tex]=\frac{1}{\sin \left(x\right)}[/tex] (expressed with sine and cosine)
[tex]\frac{1}{\sin \left(x\right)}=\csc \left(x\right)[/tex]
[tex]=\csc \left(x\right)[/tex]
Therefore, the identity has been proven true.
