Step-by-step explanation:
To answer this problem we must know the following properties.
[tex]cos(-x) = cos(x)[/tex] even function
[tex]sin(-x) = -sin(x)[/tex] odd function
[tex]cos^2(x) - sin(x)sin(-x) = 1[/tex] Because..........[tex]cos(x) = cos(-x)[/tex]
[tex]cos^2(x) + sin^2(x) = 1[/tex] Because.......... [tex]sin(-x) = -sin(x)[/tex]
By definition
[tex]cos^2 (x) + sin^2 (x) = 1[/tex]
Then, the property is demonstrated:
[tex]cos(x)cos(-x) - sin(x)sin(-x) = 1[/tex]
