Question

For any$\mathit{x}$it is true that$\mathit{c}\mathit{o}\mathit{s}\mathbf{(}\mathbf{-}\mathit{x}\mathbf{)}$has the same value as$\mathit{c}\mathit{o}\mathit{s}\mathit{x}$. We express this fact as the identity ______.

Short answer

Answer is$\mathit{c}\mathit{o}\mathit{s}\mathit{x}\mathbf{=}\mathit{c}\mathit{o}\mathit{s}\mathbf{(}\mathbf{-}\mathit{x}\mathbf{)}$

Step-by-step solution

Step 1. Given information

An incomplete trigonometric identity is given. And an example of simple equation.

Step 2. Concept used

Trigonometric functions that are represent ratios of sides of right triangles. i.e unit circle. Cosine function does not depend on the nature of input (positive or negative).

Step 3. Calculation

Let us consider the given data and simplify,

If $x$is true,

$\cos (-x)$has same value as $\cos x$

Then, we express $\cos (-x)=\cos x$