Grade 12 Math: Sum and Difference Identities
This worksheet covers sum and difference identities for trigonometric functions, designed for Grade 12 students.
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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. The sum identity for sine is sin(A + B) = sin A cos B + .
2. The difference identity for cosine is cos(A - B) = cos A cos B + .
3. To find the exact value of sin(75°), one can use the sum identity with A = 45° and B = .
1. Which of the following is equivalent to cos(30° - 45°)?
cos 30° cos 45° - sin 30° sin 45°
cos 30° cos 45° + sin 30° sin 45°
sin 30° cos 45° + cos 30° sin 45°
sin 30° cos 45° - cos 30° sin 45°
2. The expression tan(A + B) is equal to:
(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)
1. Find the exact value of sin(105°) using a sum identity. Show your steps.
2. Find the exact value of cos(15°) using a difference identity. Show your steps.
1. sin(90° - x) = cos(x)
True
False
2. cos(A + B) = cos A cos B - sin A sin B
True
False
1. If sin A = 3/5 and A is in Quadrant I, and cos B = -12/13 and B is in Quadrant II, find the exact value of sin(A - B).