How is cos (-x) = cos x

Solution:

Cosine and Sine are key terms that we use in Trigonometry. These Cosine and sine values are complementary to each other.

Cosine and sine values are complementary, thus cos a = sin (90-a).

cos (-x) = sin (90+x) {using the identity cos(A + B)}

cos (-x)= sin 90 cos x + cos 90 sin x

cos (-x)= 1*cos x + 0

cos (-x)= cos x

The number or angle will be the same as given.

Explanation 

Consider, we are beginning from the point (1,0) on the unit circle, at that moment, we will be able to see an angle of 0 radians. Now, on the movement along the circumference of the circle, and running the same angle, a first time counter clockwise, and a second time clockwise. The two angles are Θ and -Θ. We will finish with two points that can be seen lying on the very same vertical line. This will mean that one is the reflection of the other concerning the X-axis. 

It will show that the two points have coordinates (x, y) and (x, -y). Because the cosine is the x-coordinate of the points on the unit circle, we can see the two points have the same cosine and opposite sine.

The cosine is an even function; therefore, we can safely state that cos(-x) = cos x.