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

Question

Quizplus · Accepted Answer

The expression simplifies to $\sec ^ { 2 } \theta$ because $\sin ^ { 2 } \theta + \cos ^ { 2 } \theta = 1$ (a basic trigonometric identity), and $\tan ^ { 2 } \theta + 1 = \sec ^ { 2 } \theta$. So, the expression becomes $1 + \tan ^ { 2 } \theta = \sec ^ { 2 } \theta$.

Use Basic Identities to Simplify the Expression sin⁡2θ+tan⁡2θ+cos⁡2θ\sin ^ { 2 } \theta + \tan ^ { 2 } \theta + \cos ^ { 2 } \thetasin2θ+tan2θ+cos2θ

Use Basic Identities to Simplify the Expression $\sin ^ { 2 } \theta + \tan ^ { 2 } \theta + \cos ^ { 2 } \theta$