Sum and Difference Identities Worksheet
Grade 10 Math worksheet covering sum and difference identities for sine, cosine, and tangent.
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Sum and Difference Identities
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Read each question carefully and use the sum and difference identities to solve. Show all your work.
1. Which of the following is the correct identity for sin(A + B)?
sin A cos B + cos A sin B
sin A cos B - cos A sin B
cos A cos B + sin A sin B
cos A cos B - sin A sin B
2. The identity for tan(A - B) is:
(tan A + tan B) / (1 - tan A tan B)
(tan A - tan B) / (1 + tan A tan B)
(tan A - tan B) / (1 - tan A tan B)
(tan A + tan B) / (1 + tan A tan B)
3. The sum identity for cosine is cos(A + B) = cos A cos B - .
4. The difference identity for sine is sin(A - B) = sin A cos B - .
5. Use a sum or difference identity to find the exact value of cos(75°). Show your work.
6. sin(90° - x) = cos x is a true identity.
True
False
7. cos(A + B) = cos A + cos B is a true identity.
True
False
8. Given sin A = 3/5, with A in Quadrant I, and cos B = -12/13, with B in Quadrant II, find the exact value of sin(A - B).