3) Simpilfy: \( \boldsymbol{\operatorname { s i n }} \theta(\csc \theta-\sin \theta)= \) a) \( \cos ^{2} \theta \) b) \( \sin ^{2} \theta \) c) \( \cot ^{2} \theta \) d) \( \tan ^{2} \theta \)

To simplify the expression \( \sin \theta(\csc \theta - \sin \theta) \), we start by substituting \( \csc \theta \) with \( \frac{1}{\sin \theta} \): \[ \sin \theta \left( \frac{1}{\sin \theta} - \sin \theta \right) = \sin \theta \left( \frac{1 - \sin^2 \theta}{\sin \theta} \right) = 1 - \sin^2 \theta \] Using the Pythagorean identity, \( 1 - \sin^2 \theta = \cos^2 \theta \). Thus, the simplified expression is \( \cos^2 \theta \). The correct answer is: a) \( \cos^2 \theta \)