Trigonometric Identity Proofs Worksheet

Grade 12 worksheet on proving trigonometric identities, including fundamental identities, sum/difference, double angle, and half angle formulas.

Grade 12 Math TrigonometryTrigonometric Identity Proofs

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Includes

5 Short Answer

Standards

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

Topics

TrigonometryIdentitiesProofsGrade 12Math

7 sections · Free to use · Printable

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Trigonometric Identity Proofs

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Prove each of the following trigonometric identities. Show all your steps clearly and justify each transformation. Use fundamental identities, sum/difference formulas, double angle formulas, and half angle formulas as needed.

1. Prove the identity: (sin x + cos x)² = 1 + 2 sin x cos x

2. Prove the identity: tan²θ + 1 = sec²θ

3. Prove the identity: cos(A - B) = cos A cos B + sin A sin B

4. Prove the identity: sin(x + π/2) = cos x

5. Prove the identity: cos 2θ = cos²θ - sin²θ

6. Prove the identity: sin 2x = 2 sin x cos x

7. Prove the identity: tan (x/2) = (1 - cos x) / sin x

8. Prove the identity: (sin x + cos x) / (sec x + csc x) = sin x cos x