sin ⁡ u 1 + cos ⁡ u \frac{\sin\ u}{1+\cos\ u} 1 + cos u sin u

cos ⁡ u 1 + sin ⁡ u \frac{\cos\ u}{1+\sin u} 1 + sin u cos u

1 + cos ⁡ u sin ⁡ u \frac{1+\cos u}{\sin u} sin u 1 + cos u

sin ⁡ u 1 − cos ⁡ u \frac{\sin u}{1-\cos u} 1 − cos u sin u

1 + sin ⁡ u cos ⁡ u \frac{1+\sin u}{\cos u} cos u 1 + sin u

± 1 − cos ⁡ u 2 \pm\sqrt{\frac{1-\cos u}{2}} ± 2 1 − cos u <path d="M424,2478c-1.3,-0.7,-38.5,-172,-111.5,-514c-73, -342,-109.8,-513.3,-110.5,-514c0,-2,-10.7,14.3,-32,49c-4.7,7.3,-9.8,15.7,-15.5, 25c-5.7,9.3,-9.8,16,-12.5,20s-5,7,-5,7c-4,-3.3,-8.3,-7.7,-13,-13s-13,-13,-13, -13s76,-122,76,-122s77,-121,77,-121s209,968,209,968c0,-2,84.7,-361.7,254,-1079 c169.3,-717.3,254.7,-1077.7,256,-1081c4,-6.7,10,-10,18,-10H400000v40H1014.6 s-87.3,378.7,-272.6,1166c-185.3,787.3,-279.3,1182.3,-282,1185c-2,6,-10,9,-24,9 c-8,0,-12,-0.7,-12,-2z M1001 80H400000v40H1014z">

± 1 + cos ⁡ u 2 \pm\sqrt{\frac{1+\cos u}{2}} ± 2 1 + cos u <path d="M424,2478c-1.3,-0.7,-38.5,-172,-111.5,-514c-73, -342,-109.8,-513.3,-110.5,-514c0,-2,-10.7,14.3,-32,49c-4.7,7.3,-9.8,15.7,-15.5, 25c-5.7,9.3,-9.8,16,-12.5,20s-5,7,-5,7c-4,-3.3,-8.3,-7.7,-13,-13s-13,-13,-13, -13s76,-122,76,-122s77,-121,77,-121s209,968,209,968c0,-2,84.7,-361.7,254,-1079 c169.3,-717.3,254.7,-1077.7,256,-1081c4,-6.7,10,-10,18,-10H400000v40H1014.6 s-87.3,378.7,-272.6,1166c-185.3,787.3,-279.3,1182.3,-282,1185c-2,6,-10,9,-24,9 c-8,0,-12,-0.7,-12,-2z M1001 80H400000v40H1014z">

± 1 + sin ⁡ u cos ⁡ u \pm\sqrt{\frac{1+\sin u}{\cos u}} ± cos u 1 + sin u <path d="M424,2478c-1.3,-0.7,-38.5,-172,-111.5,-514c-73, -342,-109.8,-513.3,-110.5,-514c0,-2,-10.7,14.3,-32,49c-4.7,7.3,-9.8,15.7,-15.5, 25c-5.7,9.3,-9.8,16,-12.5,20s-5,7,-5,7c-4,-3.3,-8.3,-7.7,-13,-13s-13,-13,-13, -13s76,-122,76,-122s77,-121,77,-121s209,968,209,968c0,-2,84.7,-361.7,254,-1079 c169.3,-717.3,254.7,-1077.7,256,-1081c4,-6.7,10,-10,18,-10H400000v40H1014.6 s-87.3,378.7,-272.6,1166c-185.3,787.3,-279.3,1182.3,-282,1185c-2,6,-10,9,-24,9 c-8,0,-12,-0.7,-12,-2z M1001 80H400000v40H1014z">

± 1 − sin ⁡ u cos ⁡ u \pm\sqrt{\frac{1-\sin u}{\cos u}} ± cos u 1 − sin u <path d="M424,2478c-1.3,-0.7,-38.5,-172,-111.5,-514c-73, -342,-109.8,-513.3,-110.5,-514c0,-2,-10.7,14.3,-32,49c-4.7,7.3,-9.8,15.7,-15.5, 25c-5.7,9.3,-9.8,16,-12.5,20s-5,7,-5,7c-4,-3.3,-8.3,-7.7,-13,-13s-13,-13,-13, -13s76,-122,76,-122s77,-121,77,-121s209,968,209,968c0,-2,84.7,-361.7,254,-1079 c169.3,-717.3,254.7,-1077.7,256,-1081c4,-6.7,10,-10,18,-10H400000v40H1014.6 s-87.3,378.7,-272.6,1166c-185.3,787.3,-279.3,1182.3,-282,1185c-2,6,-10,9,-24,9 c-8,0,-12,-0.7,-12,-2z M1001 80H400000v40H1014z">

± 1 + cos ⁡ u 2 \pm\sqrt{\frac{1+\cos u}{2}} ± 2 1 + cos u <path d="M424,2478c-1.3,-0.7,-38.5,-172,-111.5,-514c-73, -342,-109.8,-513.3,-110.5,-514c0,-2,-10.7,14.3,-32,49c-4.7,7.3,-9.8,15.7,-15.5, 25c-5.7,9.3,-9.8,16,-12.5,20s-5,7,-5,7c-4,-3.3,-8.3,-7.7,-13,-13s-13,-13,-13, -13s76,-122,76,-122s77,-121,77,-121s209,968,209,968c0,-2,84.7,-361.7,254,-1079 c169.3,-717.3,254.7,-1077.7,256,-1081c4,-6.7,10,-10,18,-10H400000v40H1014.6 s-87.3,378.7,-272.6,1166c-185.3,787.3,-279.3,1182.3,-282,1185c-2,6,-10,9,-24,9 c-8,0,-12,-0.7,-12,-2z M1001 80H400000v40H1014z">

± 1 − sin ⁡ u 2 \pm\sqrt{\frac{1-\sin u}{2}} ± 2 1 − sin u <path d="M424,2478c-1.3,-0.7,-38.5,-172,-111.5,-514c-73, -342,-109.8,-513.3,-110.5,-514c0,-2,-10.7,14.3,-32,49c-4.7,7.3,-9.8,15.7,-15.5, 25c-5.7,9.3,-9.8,16,-12.5,20s-5,7,-5,7c-4,-3.3,-8.3,-7.7,-13,-13s-13,-13,-13, -13s76,-122,76,-122s77,-121,77,-121s209,968,209,968c0,-2,84.7,-361.7,254,-1079 c169.3,-717.3,254.7,-1077.7,256,-1081c4,-6.7,10,-10,18,-10H400000v40H1014.6 s-87.3,378.7,-272.6,1166c-185.3,787.3,-279.3,1182.3,-282,1185c-2,6,-10,9,-24,9 c-8,0,-12,-0.7,-12,-2z M1001 80H400000v40H1014z">

± 1 + sin ⁡ u cos ⁡ u \pm\sqrt{\frac{1+\sin u}{\cos u}} ± cos u 1 + sin u <path d="M424,2478c-1.3,-0.7,-38.5,-172,-111.5,-514c-73, -342,-109.8,-513.3,-110.5,-514c0,-2,-10.7,14.3,-32,49c-4.7,7.3,-9.8,15.7,-15.5, 25c-5.7,9.3,-9.8,16,-12.5,20s-5,7,-5,7c-4,-3.3,-8.3,-7.7,-13,-13s-13,-13,-13, -13s76,-122,76,-122s77,-121,77,-121s209,968,209,968c0,-2,84.7,-361.7,254,-1079 c169.3,-717.3,254.7,-1077.7,256,-1081c4,-6.7,10,-10,18,-10H400000v40H1014.6 s-87.3,378.7,-272.6,1166c-185.3,787.3,-279.3,1182.3,-282,1185c-2,6,-10,9,-24,9 c-8,0,-12,-0.7,-12,-2z M1001 80H400000v40H1014z">

± 1 − cos ⁡ u sin ⁡ u \pm\sqrt{\frac{1-\cos u}{\sin u}} ± sin u 1 − cos u <path d="M424,2478c-1.3,-0.7,-38.5,-172,-111.5,-514c-73, -342,-109.8,-513.3,-110.5,-514c0,-2,-10.7,14.3,-32,49c-4.7,7.3,-9.8,15.7,-15.5, 25c-5.7,9.3,-9.8,16,-12.5,20s-5,7,-5,7c-4,-3.3,-8.3,-7.7,-13,-13s-13,-13,-13, -13s76,-122,76,-122s77,-121,77,-121s209,968,209,968c0,-2,84.7,-361.7,254,-1079 c169.3,-717.3,254.7,-1077.7,256,-1081c4,-6.7,10,-10,18,-10H400000v40H1014.6 s-87.3,378.7,-272.6,1166c-185.3,787.3,-279.3,1182.3,-282,1185c-2,6,-10,9,-24,9 c-8,0,-12,-0.7,-12,-2z M1001 80H400000v40H1014z">

tan ⁡ A + tan ⁡ B 1 − tan ⁡ A tan ⁡ B \frac{\tan\ A+\tan B}{1-\tan A\tan B} 1 − tan A tan B tan A + tan B

tan ⁡ A − tan ⁡ B 1 + tan ⁡ A tan ⁡ B \frac{\tan A-\tan B}{1+\tan A\tan B} 1 + tan A tan B tan A − tan B

2 tan ⁡ A − 1 tan ⁡ A tan ⁡ B \frac{2\tan A-1}{\tan A\tan B} tan A tan B 2 tan A − 1

2 tan ⁡ A + 1 tan ⁡ A tan ⁡ B \frac{2\tan A+1}{\tan A\tan B} tan A tan B 2 tan A + 1

tan ⁡ A − tan ⁡ B 1 + tan ⁡ A tan ⁡ B \frac{\tan A-\tan B}{1+\tan A\tan B} 1 + tan A tan B tan A − tan B

tan ⁡ A + tan ⁡ B 1 − tan ⁡ A tan ⁡ B \frac{\tan\ A+\tan B}{1-\tan A\tan B} 1 − tan A tan B tan A + tan B

2 tan ⁡ A − 1 tan ⁡ A tan ⁡ B \frac{2\tan A-1}{\tan A\tan B} tan A tan B 2 tan A − 1

2 tan ⁡ A + 1 tan ⁡ A tan ⁡ B \frac{2\tan A+1}{\tan A\tan B} tan A tan B 2 tan A + 1

Resource Library

Math

Trigonometry

Sum And Difference Identities

Sum And Difference Formulas

Sum and Difference Formulas

Authored by Garrick Gjonovich

Mathematics

10th - 12th Grade

CCSS covered

Used 34+ times

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13 questions

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MULTIPLE SELECT QUESTION

30 sec • 1 pt

Which of the following are equivalent to cos2u?

$\cos^2u-\sin^2u$

$2\cos^2u-1$

$1-2\sin^2u$

$1-\sin^2u$

$\sin^2u-\cos^2u$

Tags

CCSS.HSF.TF.C.9

CCSS.HSF.TF.C.8

CCSS.HSF.IF.C.8

FILL IN THE BLANK QUESTION

30 sec • 1 pt

sin (A - B) = (leave no spaces when typing answer)

Tags

CCSS.HSF.TF.C.9

FILL IN THE BLANK QUESTION

30 sec • 1 pt

cos (A - B)= (leave no spaces in answer)

Tags

CCSS.HSF.TF.C.9

FILL IN THE BLANK QUESTION

30 sec • 1 pt

cos (A + B)= (leave no spaces in answer)

Tags

CCSS.HSF.TF.C.9

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

tan u/2 =

$\frac{\sin\ u}{1+\cos\ u}$

$\frac{\cos\ u}{1+\sin u}$

$\frac{1+\cos u}{\sin u}$

$\frac{\sin u}{1-\cos u}$

$\frac{1+\sin u}{\cos u}$

Tags

CCSS.HSF.TF.C.9

CCSS.HSF.TF.C.8

FILL IN THE BLANK QUESTION

30 sec • 1 pt

sin 2u = (leave no spaces in answer)

Tags

CCSS.HSF.TF.C.9

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

tan 2u =

$\frac{2\tan u}{1-\tan^2u}$

$\frac{\tan^2u}{1+\tan u}$

$\frac{2\tan u}{1+\tan^2u}$

$\frac{\tan^2u}{1-\tan u}$

Tags

CCSS.HSF.TF.C.9

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

sin u/2 =

$\pm\sqrt{\frac{1-\cos u}{2}}$

$\pm\sqrt{\frac{1+\cos u}{2}}$

$\pm\sqrt{\frac{1+\sin u}{\cos u}}$

$\pm\sqrt{\frac{1-\sin u}{\cos u}}$

Tags

CCSS.HSF.TF.C.9

CCSS.HSF.TF.C.8

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

cos u/2 =

$\pm\sqrt{\frac{1+\cos u}{2}}$

$\pm\sqrt{\frac{1-\sin u}{2}}$

$\pm\sqrt{\frac{1+\sin u}{\cos u}}$

$\pm\sqrt{\frac{1-\cos u}{\sin u}}$

Tags

CCSS.HSF.TF.C.9

10.

FILL IN THE BLANK QUESTION

30 sec • 1 pt

$\frac{1-\cos u}{\sin u}=$

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Sum and Difference Formulas

Which of the following are equivalent to cos2u?

sin (A - B) = (leave no spaces when typing answer)

cos (A - B)= (leave no spaces in answer)

cos (A + B)= (leave no spaces in answer)

tan u/2 =

sin 2u = (leave no spaces in answer)

tan 2u =

sin u/2 =

cos u/2 =

1−cos⁡usin⁡u=\frac{1-\cos u}{\sin u}=sinu1−cosu​=

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$\frac{1-\cos u}{\sin u}=$