Choose the one alternative that best completes the statement or answers the question.
Complete the identity.
-$$\frac { \sin ^ { 2 } \theta - 1 } { \sin \theta + 1 } = \text { ? }$$
A) $\sin \theta + 1$
B) $\cos ^ { 2 } \theta$
C) $\sin \theta - 1$
D) $\sin \theta$

Question

Quizplus · Accepted Answer

Using the Pythagorean identity $\sin^2\theta + \cos^2\theta = 1$, we can rewrite $\sin^2\theta - 1$ as $-\cos^2\theta$. Thus, the expression becomes $\frac{-\cos^2\theta}{\sin\theta + 1}$. Factoring $-1$ from the numerator gives $-1(\cos^2\theta)$, and using the identity $\cos^2\theta = 1 - \sin^2\theta$, we simplify the expression to $\sin\theta - 1$.

Choose the One Alternative That Best Completes the Statement or Answers