We will need to use identities to simplify and solve some trigonometric equations.Group of answer choicesTrueFalse PreviousNext

Answer

True.

In trigonometry, identities are fundamental relationships that hold true for all values of the variables involved. They are essential for simplifying complex trigonometric expressions and equations. By using identities such as the Pythagorean identities, angle sum/difference identities, and double angle identities, we can manipulate and solve trigonometric equations more effectively.

For example, when faced with an equation like $\sin^2(x) + \cos^2(x) = 1$, recognizing that this is a fundamental trigonometric identity allows us to simplify and solve the equation more easily. Similarly, other identities can be used to transform an equation into a more manageable form, ultimately leading to solutions for the variable in question. Thus, identities play a crucial role in the study and application of trigonometry.