Perform the indicated operations and simplify the result so there are no quotients.
-$\csc \theta ( \sin \theta + \cos \theta )$
A) $1 + \cot \theta$
B) $\sec \theta \csc \theta$
C) $\sin \theta \tan \theta$
D) $- 2 \tan ^ { 2 } \theta$

Question

Quizplus · Accepted Answer

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

Perform the Indicated Operations and Simplify the Result So There csc⁡θ(sin⁡θ+cos⁡θ)\csc \theta ( \sin \theta + \cos \theta )cscθ(sinθ+cosθ)

Perform the Indicated Operations and Simplify the Result So There $\csc \theta ( \sin \theta + \cos \theta )$