Perform the indicated operations and simplify the result so there are no quotients.
-$\tan ^ { 2 } \theta \csc ^ { 2 } \theta$
A) $\sec ^ { 2 } \theta$
B) $\cos ^ { 3 } \theta$
C) $\tan ^ { 2 } \theta$
D) $\sin \theta$

Question

Quizplus · Accepted Answer

Using trigonometric identities, $\tan^2 \theta = \sin^2 \theta / \cos^2 \theta$ and $\csc^2 \theta = 1 / \sin^2 \theta$. Multiplying these gives $\sin^2 \theta / \cos^2 \theta \times 1 / \sin^2 \theta = 1 / \cos^2 \theta = \sec^2 \theta$.

Perform the Indicated Operations and Simplify the Result So There tan⁡2θcsc⁡2θ\tan ^ { 2 } \theta \csc ^ { 2 } \thetatan2θcsc2θ

Perform the Indicated Operations and Simplify the Result So There $\tan ^ { 2 } \theta \csc ^ { 2 } \theta$