Sum and Difference Formulae
Math ⇒ Trigonometry
Sum and Difference Formulae starts at 11 and continues till grade 12.
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See sample questions for grade 12
Describe a real-world application where sum and difference formulae are used.
Explain why the sum and difference formulae are important in trigonometry.
Prove that cos(90° - x) = sin x using sum and difference formulae.
Prove that tan(A + B) = (tan A + tan B) / (1 - tan A tan B).
Given tan A = 1 and tan B = 2, find tan(A + B).
If cos A = 0.6 and sin B = 0.8, with both A and B in the first quadrant, and sin A = 0.8, cos B = 0.6, find cos(A - B).
If sin 30° = 1/2 and cos 45° = √2/2, calculate sin(30° + 45°).
If sin 75° = sin(45° + 30°), use the sum formula to find its value.
Which of the following is NOT a correct sum or difference formula?
(1) sin(A + B) = sin A cos B + cos A sin B
(2) cos(A - B) = cos A cos B + sin A sin B
(3) tan(A - B) = (tan A - tan B) / (1 + tan A tan B)
(4) cos(A + B) = cos A cos B - sin A sin B
Which of the following is the correct formula for cos(A - B)?
(1) cos A cos B + sin A sin B
(2) cos A cos B - sin A sin B
(3) cos A sin B + sin A cos B
(4) sin A sin B - cos A cos B
Which of the following is the correct formula for cos(A + B)?
(1) cos A cos B + sin A sin B
(2) cos A cos B - sin A sin B
(3) cos A sin B + sin A cos B
(4) sin A sin B - cos A cos B
Which of the following is the correct formula for sin(A - B)?
(1) sin A cos B + cos A sin B
(2) sin A cos B - cos A sin B
(3) sin A sin B - cos A cos B
(4) sin A sin B + cos A cos B
Fill in the blank: cos(A - B) = _________________.
Fill in the blank: cos(A + B) = _________________.
Fill in the blank: sin(A + B) = _________________.
Fill in the blank: tan(A - B) = _________________.
True or False: cos(A + B) = cos A cos B + sin A sin B.
True or False: sin(A - B) = sin A cos B - cos A sin B.
True or False: tan(A + B) = (tan A + tan B) / (1 + tan A tan B).
True or False: The sum and difference formulae are only valid for angles measured in degrees.
