Simplify the following expression algebraically. $7 \cos ( \pi + x )$
A) $- 7 \sin x$
B) $- 7 \cos x$
C) $7 \cos x$
D) $\frac { 3 } { 2 } \cos x$
E) $- \frac { 3 } { 2 } \cos x$

Question

Simplify the following expression algebraically.​ $7 \cos ( \pi + x )$ ​
A) $- 7 \sin x$
B) $- 7 \cos x$
C) $7 \cos x$
D) $\frac { 3 } { 2 } \cos x$
E) $- \frac { 3 } { 2 } \cos x$

Quizplus · Accepted Answer

The trigonometric identity for cosine with an angle sum, $\cos(\alpha + \beta)$, states that $\cos(\alpha + \beta) = \cos \alpha \cos \beta - \sin \alpha \sin \beta$. Applying this to $\cos(\pi + x)$, we get $\cos \pi \cos x - \sin \pi \sin x$. Since $\cos \pi = -1$ and $\sin \pi = 0$, the expression simplifies to $-1 \cdot \cos x = -\cos x$. Therefore, $7 \cos(\pi + x) = 7(-\cos x) = -7 \cos x$.

Simplify the Following Expression Algebraically 7cos⁡(π+x)7 \cos ( \pi + x )7cos(π+x)

Simplify the Following Expression Algebraically $7 \cos ( \pi + x )$