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

Question

Quizplus · Accepted Answer

The expression simplifies to $1 + \cot x$ because $\csc x = \frac{1}{\sin x}$, so $\csc x (\sin x + \cos x) = \frac{1}{\sin x} \sin x + \frac{1}{\sin x} \cos x = 1 + \cot x$.

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