Write the expression in terms of sine and cosine, and simplify so that no quotients appear in the final expression.
-$\sin ^ { 2 } \theta + \tan ^ { 2 } \theta + \cos ^ { 2 } \theta$
A) $\sin \theta$
B) $\tan ^ { 2 } \theta$
C) $\sec ^ { 2 } \theta$
D) $\cos ^ { 3 } \theta$

Question

Quizplus · Accepted Answer

The given expression can be simplified using trigonometric identities. We know that $\sin^2\theta + \cos^2\theta = 1$ and $\tan^2\theta = \sec^2\theta - 1$. Substituting these into the original expression gives $1 + \sec^2\theta - 1$, which simplifies to $\sec^2\theta$.

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