# Precalculus : Use Odd-Even Identities

## Example Questions

### Example Question #1 : Fundamental Trigonometric Identities

Which of the following statements is false?

Explanation:

Of the six trigonometric functions, four are odd, meaning . These four are:

• sin x
• tan x
• cot x
• csc x

That leaves two functions which are even, which means that . These are:

• cos x
• sec x

Of the aforementioned, only  is incorrect, since secant is an even function, which implies that

### Example Question #1 : Use Odd Even Identities

Find the value of .

Explanation:

Rewrite  by odd and even identities.

Use the difference identity of sine, and choose the special angles 45 and 30, since their difference equals to 15.

### Example Question #1 : Use Odd Even Identities

Simplify:

Explanation:

Write the even and odd identities for sine and cosine.

Rewrite the expression  and evaluate.

Simplify: