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Sum & Difference Formulas — Easy Worksheet 2
Grade 12 · MathSheets Name: ____________________ Date: __________
Give exact answers. Write radicals like (√6 + √2)/4 or 2 - √3, and fractions in simplest form.
How to solve
sin(A ± B) = sin A cos B ± cos A sin B, cos(A ± B) = cos A cos B ∓ sin A sin B, tan(A ± B) = tan A ± tan B1 ∓ tan A tan B. Split the angle into standard angles, e.g. 75° = 45° + 30°, and substitute the exact values.
Example
Use a sum or difference formula to find the exact value of sin(15°).
Answer: √6 - √24
Not quite. The answer is
💡 sin(15°) = sin(45° − 30°) = sin 45° cos 30° − cos 45° sin 30° = (√22)(√32) − (√22)(12) = √64 − √24 = √6 − √24.
✓ Correct!
Not quite. The answer is
💡 sin(15°) = sin(45° − 30°) = sin 45° cos 30° − cos 45° sin 30° = (√22)(√32) − (√22)(12) = √64 − √24 = √6 − √24.
💡 How to solve: Sum & Difference Formulas
sin(A ± B) = sin A cos B ± cos A sin B, cos(A ± B) = cos A cos B ∓ sin A sin B, tan(A ± B) = tan A ± tan B1 ∓ tan A tan B. Split the angle into standard angles, e.g. 75° = 45° + 30°, and substitute the exact values.
Try a similar one
Use a sum or difference formula to find the exact value of sin(75°).
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 This is the right side of sin(A − B) = sin A cos B − cos A sin B with A = 50° and B = 5°. So it equals sin(50° − 5°) = sin(45°) = √22.
✓ Correct!
Not quite. The answer is
💡 This is the right side of sin(A − B) = sin A cos B − cos A sin B with A = 50° and B = 5°. So it equals sin(50° − 5°) = sin(45°) = √22.
💡 How to solve: Sum & Difference Formulas
sin(A ± B) = sin A cos B ± cos A sin B, cos(A ± B) = cos A cos B ∓ sin A sin B, tan(A ± B) = tan A ± tan B1 ∓ tan A tan B. Split the angle into standard angles, e.g. 75° = 45° + 30°, and substitute the exact values.
Try a similar one
Use a sum or difference formula to find the exact value of sin(15°).
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 This is the right side of sin(A − B) = sin A cos B − cos A sin B with A = 85° and B = 40°. So it equals sin(85° − 40°) = sin(45°) = √22.
✓ Correct!
Not quite. The answer is
💡 This is the right side of sin(A − B) = sin A cos B − cos A sin B with A = 85° and B = 40°. So it equals sin(85° − 40°) = sin(45°) = √22.
💡 How to solve: Sum & Difference Formulas
sin(A ± B) = sin A cos B ± cos A sin B, cos(A ± B) = cos A cos B ∓ sin A sin B, tan(A ± B) = tan A ± tan B1 ∓ tan A tan B. Split the angle into standard angles, e.g. 75° = 45° + 30°, and substitute the exact values.
Try a similar one
Use a sum or difference formula to find the exact value of sin(75°).
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 cos(15°) = cos(45° − 30°) = cos 45° cos 30° + sin 45° sin 30° = (√22)(√32) + (√22)(12) = √64 + √24 = √6 + √24.
✓ Correct!
Not quite. The answer is
💡 cos(15°) = cos(45° − 30°) = cos 45° cos 30° + sin 45° sin 30° = (√22)(√32) + (√22)(12) = √64 + √24 = √6 + √24.
💡 How to solve: Sum & Difference Formulas
sin(A ± B) = sin A cos B ± cos A sin B, cos(A ± B) = cos A cos B ∓ sin A sin B, tan(A ± B) = tan A ± tan B1 ∓ tan A tan B. Split the angle into standard angles, e.g. 75° = 45° + 30°, and substitute the exact values.
Try a similar one
Use a sum or difference formula to find the exact value of cos(75°).
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 This is the right side of sin(A + B) = sin A cos B + cos A sin B with A = 50° and B = 40°. So it equals sin(50° + 40°) = sin(90°) = 1.
✓ Correct!
Not quite. The answer is
💡 This is the right side of sin(A + B) = sin A cos B + cos A sin B with A = 50° and B = 40°. So it equals sin(50° + 40°) = sin(90°) = 1.
💡 How to solve: Sum & Difference Formulas
sin(A ± B) = sin A cos B ± cos A sin B, cos(A ± B) = cos A cos B ∓ sin A sin B, tan(A ± B) = tan A ± tan B1 ∓ tan A tan B. Split the angle into standard angles, e.g. 75° = 45° + 30°, and substitute the exact values.
Try a similar one
Use a sum or difference formula to find the exact value of cos(15°).
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 This is the right side of sin(A + B) = sin A cos B + cos A sin B with A = 10° and B = 50°. So it equals sin(10° + 50°) = sin(60°) = √32.
✓ Correct!
Not quite. The answer is
💡 This is the right side of sin(A + B) = sin A cos B + cos A sin B with A = 10° and B = 50°. So it equals sin(10° + 50°) = sin(60°) = √32.
💡 How to solve: Sum & Difference Formulas
sin(A ± B) = sin A cos B ± cos A sin B, cos(A ± B) = cos A cos B ∓ sin A sin B, tan(A ± B) = tan A ± tan B1 ∓ tan A tan B. Split the angle into standard angles, e.g. 75° = 45° + 30°, and substitute the exact values.
Try a similar one
Use a sum or difference formula to find the exact value of cos(75°).
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 sin(75°) = sin(45° + 30°) = sin 45° cos 30° + cos 45° sin 30° = (√22)(√32) + (√22)(12) = √64 + √24 = √6 + √24.
✓ Correct!
Not quite. The answer is
💡 sin(75°) = sin(45° + 30°) = sin 45° cos 30° + cos 45° sin 30° = (√22)(√32) + (√22)(12) = √64 + √24 = √6 + √24.
💡 How to solve: Sum & Difference Formulas
sin(A ± B) = sin A cos B ± cos A sin B, cos(A ± B) = cos A cos B ∓ sin A sin B, tan(A ± B) = tan A ± tan B1 ∓ tan A tan B. Split the angle into standard angles, e.g. 75° = 45° + 30°, and substitute the exact values.
Try a similar one
Use a sum or difference formula to find the exact value of cos(15°).
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 This is the right side of sin(A + B) = sin A cos B + cos A sin B with A = 10° and B = 20°. So it equals sin(10° + 20°) = sin(30°) = 12.
✓ Correct!
Not quite. The answer is
💡 This is the right side of sin(A + B) = sin A cos B + cos A sin B with A = 10° and B = 20°. So it equals sin(10° + 20°) = sin(30°) = 12.
💡 How to solve: Sum & Difference Formulas
sin(A ± B) = sin A cos B ± cos A sin B, cos(A ± B) = cos A cos B ∓ sin A sin B, tan(A ± B) = tan A ± tan B1 ∓ tan A tan B. Split the angle into standard angles, e.g. 75° = 45° + 30°, and substitute the exact values.
Try a similar one
Use a sum or difference formula to find the exact value of sin(75°).
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
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Sum & Difference Formulas — Easy Worksheet 2
Give exact answers. Write radicals like (√6 + √2)/4 or 2 - √3, and fractions in simplest form.