Use the fundamental identities to simplify the expression.
-$\tan ^ { 2 } \theta \csc ^ { 2 } \theta$
A) $\sec ^ { 2 } \theta$
B) $\tan ^ { 2 } \theta$
C) $\cos ^ { 3 } \theta$
D) $\sin \theta$

Question

Quizplus · Accepted Answer

The expression can be simplified using the identity $\csc^2\theta = 1 + \tan^2\theta$. Since $\csc^2\theta = 1/\sin^2\theta$, and $\tan^2\theta = \sin^2\theta/\cos^2\theta$, multiplying $\tan^2\theta$ by $\csc^2\theta$ simplifies to $\sec^2\theta$ because $\sec^2\theta = 1/\cos^2\theta$.

Use the Fundamental Identities to Simplify the Expression tan⁡2θcsc⁡2θ\tan ^ { 2 } \theta \csc ^ { 2 } \thetatan2θcsc2θ

Use the Fundamental Identities to Simplify the Expression $\tan ^ { 2 } \theta \csc ^ { 2 } \theta$