Simplify $\sin ^{2} x+\sin ^{2} x \cot ^{2} x$
So, the simplified form of the given expression is \(\boxed{1}\)
Step 1 :Rewrite the given expression as \(\sin ^{2} x+\sin ^{2} x \frac{\cos ^{2} x}{\sin ^{2} x}\)
Step 2 :Cancel out the \(\sin ^{2} x\) in the denominator and numerator, leaving us with \(\sin ^{2} x + \cos ^{2} x\)
Step 3 :According to the Pythagorean identity, \(\sin ^{2} x + \cos ^{2} x = 1\)
Step 4 :So, the simplified form of the given expression is \(\boxed{1}\)