Answer
(d). $\frac{1}{\sin\theta} - \frac{\sin^{2}\theta}{\sin\theta}$
is a valid step
Work Step by Step
To prove any identity, we begin with one side i.e. L.S. and try to transform it to other side i.e. R.S.
L.S. of the given expression is-
$\frac{1}{\sin\theta} - \sin\theta$
To add both, we will multiply the term $\sin\theta$ by $\frac{\sin\theta}{\sin\theta}$, hence the expression becomes-
$\frac{1}{\sin\theta} - \sin\theta.\frac{\sin\theta}{\sin\theta}$
= $\frac{1}{\sin\theta} - \frac{\sin^{2}\theta}{\sin\theta}$
Thus option (d) is a valid step.
