Step-by-step explanation:
[tex]\frac{1-\sin ^2\left(x\right)}{1+\sin \left(x\right)}=1-\frac{1}{\csc \left(x\right)}[/tex]
[tex]\frac{1-\sin ^2\left(x\right)}{1+\sin \left(x\right)}[/tex]
[tex]=1-\sin \left(x\right)[/tex]
⇒ [tex]\sin \left(x\right)=\frac{1}{\csc \left(x\right)}[/tex]
[tex]=1-\frac{1}{\csc \left(x\right)}[/tex]
