Write each expression in factored form as an algebraic expression of a single trigonometric function.
-$$\frac { \sin ^ { 2 } x - 1 } { 1 + \sin x }$$
A) $\sin ^ { 2 } x + 1$
B) $\sin x + 1$
C) $\sin x - 1$
D) $- \cos x$

Question

Quizplus · Accepted Answer

The given expression can be simplified using the Pythagorean identity $\sin^2x + \cos^2x = 1$. Substituting $\sin^2x = 1 - \cos^2x$ into the expression, we get $\frac{1 - \cos^2x - 1}{1 + \sin x}$, which simplifies to $\frac{-\cos^2x}{1 + \sin x}$. Recognizing that $\cos^2x = (1 - \sin^2x)$ and simplifying further, we find that the expression simplifies to $\sin x - 1$, using trigonometric identities and algebraic manipulation.

Write Each Expression in Factored Form as an Algebraic Expression sin⁡2x−11+sin⁡x\frac { \sin ^ { 2 } x - 1 } { 1 + \sin x }1+sinxsin2x−1​

Write Each Expression in Factored Form as an Algebraic Expression $\frac { \sin ^ { 2 } x - 1 } { 1 + \sin x }$