Show that the equation is not an identity by finding a value of x for which both sides are defined but not equal.
-$\cos ( x + \pi ) = \cos x$
A) 0
B) $\frac { \pi } { 2 }$
C) $- \frac { \pi } { 2 }$
D) $\frac { 3 \pi } { 2 }$

Question

Quizplus · Accepted Answer

The equation $\cos(x + \pi) = \cos x$ is not an identity because $\cos(x + \pi) = -\cos x$. For $x = 0$, $\cos(0 + \pi) = \cos(\pi) = -1$, but $\cos(0) = 1$, showing the two sides are not equal.

Show That the Equation Is Not an Identity by Finding cos⁡(x+π)=cos⁡x\cos ( x + \pi ) = \cos xcos(x+π)=cosx

Show That the Equation Is Not an Identity by Finding $\cos ( x + \pi ) = \cos x$