Trigonometric Proofs Worksheet

A Grade 10 math worksheet focusing on proving trigonometric identities and solving trigonometric equations.

Grade 10 Math TrigonometryTrigonometric Proofs

Use This Worksheet

Includes

Short AnswerFill in the BlanksMatchingTrue / FalseMultiple Choice

Standards

CCSS.MATH.CONTENT.HSG.SRT.C.8CCSS.MATH.CONTENT.HSF.TF.C.8

Topics

mathtrigonometryproofsidentitiesgrade 10

7 sections · Free to use · Printable

Name:

Date:

Score:

Prove the following trigonometric identities. Show all your steps clearly.

1. Prove that: sin(θ)cot(θ) = cos(θ)

2. Prove that: (1 - sin²(θ))/cos(θ) = cos(θ)

3. Prove that: tan(θ) + cot(θ) = sec(θ)csc(θ)

4. The Pythagorean identity states that sin²(θ) + cos²(θ) = .

5. The reciprocal of sin(θ) is .

6. The quotient identity for tan(θ) is sin(θ) / .

Match each expression on the left with its equivalent identity on the right.

7. sec(θ)

a. 1/sin(θ)

8. csc(θ)

b. 1/cos(θ)

9. cot(θ)

c. cos(θ)/sin(θ)

10. The identity 1 + tan²(θ) = sec²(θ) is true.

True

False

11. sin(2θ) = 2sin(θ)cos(θ) is a double angle identity.

True

False

12. Which of the following is equivalent to csc(θ)cos(θ)?

tan(θ)

cot(θ)

sec(θ)

sin(θ)