Step-by-step explanation:
Recall that
[tex]\sin (\frac{\pi}{2} - x) = \cos x[/tex]
[tex]\cos (\frac{\pi}{2} - x) = \sin x[/tex]
So we can rewrite the given expression as
[tex]\dfrac{\cos^2 x}{\sin^2 x} + (\sin^2 x + \cos^2 x)[/tex]
[tex]\Rightarrow \dfrac{\cos^2 x}{\sin^2 x} + 1[/tex]
or
[tex]\dfrac{\cos^2 x + \sin^2 x}{\sin^2 x} = \dfrac{1}{\sin^2 x} = \csc^2 x[/tex]
