Write the expression in terms of sine and cosine, and simplify so that no quotients appear in the final expression.
-$\sin ^ { 2 } x \left( \cot ^ { 2 } x + 1 \right)$
A) $- 1$
B) $\tan ^ { 2 } x$
C) $\cos ^ { 2 } x + 1$
D) 1

Question

Quizplus · Accepted Answer

The expression can be simplified using trigonometric identities. The identity $\cot^2x + 1 = \csc^2x$ can be used, where $\csc x = \frac{1}{\sin x}$. Thus, $\sin^2x(\cot^2x + 1) = \sin^2x \cdot \csc^2x$. Since $\csc x = \frac{1}{\sin x}$, $\csc^2x = \frac{1}{\sin^2x}$, making the expression $\sin^2x \cdot \frac{1}{\sin^2x} = 1$.

Write the Expression in Terms of Sine and Cosine, and Simplify