Perform the indicated operations and simplify the result so there are no quotients.
-$\tan \theta ( \cot \theta - \cos \theta )$
A) $1 - \sin \theta$
B) 1
C) 0
D) $- \sec ^ { 2 } \theta$

Question

Quizplus · Accepted Answer

The expression simplifies to $1 - \sin \theta$ because $\tan \theta (\cot \theta - \cos \theta) = \tan \theta \cot \theta - \tan \theta \cos \theta = 1 - \sin \theta$. This is because $\tan \theta \cot \theta = 1$ and $\tan \theta \cos \theta = \sin \theta$.

Perform the Indicated Operations and Simplify the Result So There tan⁡θ(cot⁡θ−cos⁡θ)\tan \theta ( \cot \theta - \cos \theta )tanθ(cotθ−cosθ)

Perform the Indicated Operations and Simplify the Result So There $\tan \theta ( \cot \theta - \cos \theta )$