Explain trigonometric identities and equations

Trigonometric identities are equations involving trigonometric functions that are true for all values of the variables for which the functions are defined. They are fundamental relationships that hold universally, such as $\sin^2(\theta) + \cos^2(\theta) = 1$.

Trigonometric equations, on the other hand, are equations involving trigonometric functions that are true only for specific values of the variables. Solving a trigonometric equation means finding those particular values of the angle that satisfy the equation, for example, finding $\theta$ when $\sin(\theta) = \frac{1}{2}$.