We have
[tex]\tan ^2(x)csc^2(x)=\frac{1}{\cos ^2(x)}[/tex][tex]\tan (x)=\frac{\sin(x)}{\cos(x)}[/tex][tex]\csc (x)=\frac{1}{\sin (x)}[/tex]we substitute the equalities given above
[tex]\frac{\sin^2(x)}{\cos^2(x)}\cdot\frac{1^2}{\sin^2(x)}=\frac{\sin^2(x)}{\sin^2(x)\cos^2(x)}=\frac{1}{\cos ^2(x)}[/tex]as we can see we verify the identity because we obtain the same result
