Cosine Identity

In the applet below, the graph of the function [math]f\left(x\right)=cos\left(x\right)[/math] is displayed. [br][br]Place the BIG WHITE POINT anywhere you'd like prior to sliding the slider. [br][br]Answer the question that follows.
1.
Write a new trigonometric identity that expresses the relationship between [math]cos\left(x\right)[/math] and [math]cos\left(-x\right)[/math].
2.
What else can you conclude about the parent cosine function [math]f\left(x\right)=cos\left(x\right)[/math]? [br]For a hint, [url=https://www.geogebra.org/m/A5S7naz3]click here[/url].
Quick Demo: 0:36 sec to 1:05 sec (BGM: Andy Hunter)
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Information: Cosine Identity