Answer
Verified below.
Work Step by Step
We know that, $\sin \theta =\frac{1}{\csc \theta }$.
Therefore, we can rewrite the equation:
$\sin \theta \csc \theta -{{\cos }^{2}}\theta $, as:
$\begin{align}
& \sin \theta \csc \theta -{{\cos }^{2}}\theta =\sin \theta \left( \frac{1}{\sin \theta } \right)-{{\cos }^{2}}\theta \\
& =1-{{\cos }^{2}}\theta \\
& ={{\sin }^{2}}\theta
\end{align}$
Therefore, from (1) we get;
$\sin \theta \csc \theta -{{\cos }^{2}}\theta ={{\sin }^{2}}\theta $
