Question

Cos x cos(-x)-sin x sin(-x)=1 please certify the identity with steps!!!!!

Answer 1

Explanation:

To answer this problem we must know the following properties.

`cos(-x) = cos(x)` even function

`sin(-x) = -sin(x)` odd function

`cos^2(x) - sin(x)sin(-x) = 1` Because..........
`cos(x) = cos(-x)`

`cos^2(x) + sin^2(x) = 1` Because..........
`sin(-x) = -sin(x)`

By definition

`cos^2 (x) + sin^2 (x) = 1`

Then, the property is demonstrated:

`cos(x)cos(-x) - sin(x)sin(-x) = 1`