Trignometric identities

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Last updated 8:25 AM on 5/29/26
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55 Terms

1
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sin²A + cos²A

1

2
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1 + tan²A

sec²A

3
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1 + cot²A

cosec²A

4
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tanA

sinA/cosA

5
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cotA

cosA/sinA

6
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sinA

1/cosecA

7
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cosA

1/secA

8
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tanA

1/cotA

9
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sin2A

2sinAcosA

10
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sin2A

2tanA/(1+tan²A)

11
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cos2A

cos²A - sin²A

12
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cos2A

2cos²A - 1

13
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cos2A

1 - 2sin²A

14
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cos2A

(1-tan²A)/(1+tan²A)

15
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tan2A

2tanA/(1-tan²A)

16
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sin(A/2)

√((1-cosA)/2)

17
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cos(A/2)

√((1+cosA)/2)

18
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tan(A/2)

√((1-cosA)/(1+cosA))

19
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tan(A/2)

sinA/(1+cosA)

20
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tan(A/2)

(1-cosA)/sinA

21
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sin3A

3sinA - 4sin³A

22
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cos3A

4cos³A - 3cosA

23
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tan3A

(3tanA - tan³A)/(1 - 3tan²A)

24
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sin(A+B)

sinAcosB + cosAsinB

25
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sin(A-B)

sinAcosB - cosAsinB

26
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cos(A+B)

cosAcosB - sinAsinB

27
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cos(A-B)

cosAcosB + sinAsinB

28
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tan(A+B)

(tanA+tanB)/(1-tanAtanB)

29
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tan(A-B)

(tanA-tanB)/(1+tanAtanB)

30
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2sinAcosB

sin(A+B) + sin(A-B)

31
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2cosAsinB

sin(A+B) - sin(A-B)

32
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2cosAcosB

cos(A+B) + cos(A-B)

33
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2sinAsinB

cos(A-B) - cos(A+B)

34
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sinC + sinD

2sin((C+D)/2)cos((C-D)/2)

35
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sinC - sinD

2cos((C+D)/2)sin((C-D)/2)

36
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cosC + cosD

2cos((C+D)/2)cos((C-D)/2)

37
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cosC - cosD

-2sin((C+D)/2)sin((C-D)/2)

38
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sin²A

(1 - cos2A)/2

39
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cos²A

(1 + cos2A)/2

40
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tan²A

(1 - cos2A)/(1 + cos2A)

41
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sin(-A)

-sinA

42
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cos(-A)

cosA

43
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tan(-A)

-tanA

44
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sin(90-A)

cosA

45
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cos(90-A)

sinA

46
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tan(90-A)

cotA

47
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sin(90+A)

cosA

48
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cos(90+A)

-sinA

49
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tan(90+A)

-cotA

50
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sin(180-A)

sinA

51
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cos(180-A)

-cosA

52
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tan(180-A)

-tanA

53
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sin(180+A)

-sinA

54
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cos(180+A)

-cosA

55
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tan(180+A)

tanA