# Lesson Worksheet: Simplifying Trigonometric Expressions Using Trigonometric Identities Mathematics

In this worksheet, we will practice simplifying trigonometric expressions by applying trigonometric identities.

Q1:

Simplify .

• A
• B
• C
• D1

Q2:

Simplify .

• A
• B
• C
• D

Q3:

Simplify .

• A
• B
• C
• D

Q4:

Simplify .

• A
• B
• C
• D

Q5:

Simplify .

• A
• B
• C
• D1

Q6:

Simplify .

• A
• B
• C1
• D

Q7:

Simplify .

• A
• B
• C
• D

Q8:

Simplify .

• A
• B
• C
• D

Q9:

Simplify .

• A
• B
• C
• D

Q10:

Which of the following expressions is equivalent to ?

• A
• B
• C
• D
• E

Q11:

Is an identity or an equation?

• Aan equation
• Ban identity

Q12:

Which of the following is not a trigonometric identity?

• A
• B

Q13:

Which of the following expressions is equal to ?

• A
• B
• C
• D
• E

Q14:

Which of the following is a trigonometric identity?

• A
• B

Q15:

Simplify .

• A
• B
• C1
• D

Q16:

Simplify .

Q17:

Simplify in its simplest form.

Q18:

Simplify .

Q19:

Simplify .

Q20:

Simplify .

• A
• B
• C
• D

Q21:

Consider the identity . We can use this to derive two new identities.

First, divide both sides of the identity by to find an identity in terms of and .

• A
• B
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• D
• E

Now, divide both sides of the identity through by to find an identity in terms of and .

• A
• B
• C
• D
• E

Q22:

The figure shows a unit circle and a radius with the lengths of its - and -components. Use the Pythagorean theorem to derive an identity connecting the lengths 1, , and . • A
• B
• C
• D
• E

Q23:

For any , what is ?

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• C
• D
• E

Q24:

For any , what is ?

• A
• B
• C
• D
• E

Q25:

For any , what is ?

• A
• B
• C
• D
• E