Question

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

Answer 1

Step-by-step 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:

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