# How is cos(-x) = cos(x) ?

Trigonometric ratios deals with the relation between the angles and sides of a triangle.

## Answer: cos(-x) = cos(x)

Using the complimentary angle properties of sine and cosine functions, let's prove it.

**Explanation:**

Cosine and Sine values are complimentary.

Thus, cos a = sin(90° - a)

⇒ cos(-x) = sin(90° +x)

We know that, sin(A + B) = sin A cos B + cos A sin B

Thus, using this formula we can expand sin(90° + x)

= sin 90° × cosx + cos90° × sin x

= 1 × cosx + 0 × sin x (Since, sin 90° = 1, cos 90° = 0)

= cos x

**Alternative Explanation:**

Cosine function is an even function that is mirrored perfectly around the y-axis.

So, for every absolute value on the x-axis, the value of the y will be the same - whether the point x is chosen on the positive x-axis or the negative x-axis.

### Thus, cos(-x) = cos(x)