5.2 Verifying Trigonometric Identities

Hints for Verifying Identities

1. Learn the fundamental Identities in Section 5.1 and be aware of equivalent

forms.

2. Try to rewrite the more complicated side.

3. It is often helpful to express all trig functions in the equation in terms of sine

and cosine.

4. Factoring is often necessary as in

5. Rewriting fraction sums as a single fraction is also often necessary as in

6. Renaming a fraction by multiplying numerator and denominator by a

difference or sum, as in multiply

Note: Verifying an identity is not the same as solving an equation!!

Techniques of “adding to both sides” or “clearing fractions” cannot be used on identities. Renaming must always work with only one side.

Verifying Identities by Working with One Side

Work with only one side and rewrite it to match the other side.

Example

Verify that the following equation is an identity

Example

Verify that the following equation is an identity.

Example

Verify that the following equation is an identity.

Example

Verify that the following equation is an identity.

Verifying an Identity by working with Both Sides

When both sides are “messy”, we can work individually with each side to get both sides equal to a third expression.

Example

Verify that the following equation is an identity.