Trigonometric Proofs Worksheet
A Grade 10 math worksheet focusing on proving trigonometric identities and solving trigonometric equations.
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Trigonometric Proofs Worksheet
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Date:
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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)
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