Question

An equation is called an identity if it is valid for values of the variable. The equation$\mathbf{2}\mathit{x}\mathbf{=}\mathit{x}\mathbf{+}\mathit{x}$ is an algebraic identity, and the equation $\mathit{s}\mathit{i}{\mathit{n}}^{\mathbf{2}}\mathit{x}\mathbf{+}\mathit{c}\mathit{o}{\mathit{s}}^{\mathbf{2}}\mathit{x}\mathbf{=}$________ is a trigonometric identity.

Short answer

Answer is 1.

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. The identity given in the question can be written as-

$si{n}^{2}x+co{s}^{2}x=1$

Step 3. Calculation

The identity is-

$si{n}^{2}x+co{s}^{2}x=1$

If we compare it with identity given in the question then the answer is 1