Trig Identities

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72 Terms

1
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csc x=

1/sin

2
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sec x=

1/cos

3
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cot x=

1/tanx

4
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tan x=

sinx/cosx

5
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cotx=

cosx/sinx

6
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sin^2x+cos^2x=

1

7
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sin(-x)

-sinx

8
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tan^2 x+1=

sec^2 x

9
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1+cot^2 x=

csc^2 x

10
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cos (-x)

cosx

11
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tan (-x)

-tanx

12
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sin (pi/2 - u)=

cos u

13
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cos (pi/2-u)=

sin u

14
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tan (pi/2-u)

cot u

15
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cot (pi/2-u)

tan u

16
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csc (pi/2 - u)

sec u

17
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sin (s+t)

sin s cos t+ cos s sin t

18
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sin (s-t)

sin s cos t- cos s sin t

19
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cos (s+t)

cos s cos t- sin s sin t

20
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cos (s-t)

cos s cos t+ sin s sin t

21
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tan (s+t)

(tan s + tan t )/ (1-tan s tan t)

22
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tan (s-t)

(tan s - tan t)/(1+ tan s tan t)

23
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sin u cos v

1/2 [sin (u+v) + sin (u-v)]

24
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cos u sin v

1/2 [sin (u+v)- sin (u-v)]

25
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cos u cos v

1/2[cos (u+v)+ cos (u-v)]

26
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sin u sin v

1/2 [cos (u+v)- cos (u+v)]

27
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sin x+ sin y

2sin (x+y)/2 cos (x-y)/2

28
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sinx- siny

2 cos (x+y)/2cos (x-y)/2

29
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cosx+ cos y

2 cos (x+y)/2 cos (x-y)/2

30
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cos x- cos y

-2sin (x+y)/2 sin (x-y)/2

31
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sin 2x

2sin x cosx

32
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cos2x

cos^2 x- sin^2 x; = 1-2sin^2x; = 2 cos^2 x-1

33
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tan 2x

2tanx/(1-tan^2 x)

34
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sin^2 x

(1-cos 2x)/2

35
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tan ^2 x

(1-cos2x)/(1+cos2x)

36
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sin u/2

+- sqrt (1-cos u)/2

37
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cos u/2

+- sqrt (1+cos u)/2

38
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tan u/2

(1-cos u)/sin u; = sin u/ (1+cos u)

39
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(Reciprocal) sin u

1/csc u

40
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(Reciprocal) cos u

1/sec u

41
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(Reciprocal) tan u

1/cot u

42
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(Reciprocal) csc u

1/sin u

43
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(Reciprocal) sec u

1/cos u

44
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(Reciprocal) cot u

1/tan u

45
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(Quotient) tan u

sin u/cos u

46
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(Quotient) cot u

cos u/sin u

47
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(Pythagorean) sin² u+cos² u

1

48
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(Pythagorean) 1+tan² u

sec² u

49
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(Pythagorean) 1+cot² u

csc² u

50
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(Cofunction) sin(Ď€/2-u)

cos u

51
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(Cofunction) cos(Ď€/2-u)

sin u

52
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(Cofunction) tan(Ď€/2-u)

cot u

53
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(Cofunction) cot(Ď€/2-u)

tan u

54
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(Cofunction) sec(Ď€/2-u)

cos u

55
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(Cofunction) csc(Ď€/2-u)

sin u

56
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(Even/Odd) sin(-u)

-sin u

57
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(Even/Odd) cos(-u)

cos u

58
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(Even/Odd) tan(-u)

-tan u

59
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(Even/Odd) csc(-u)

-csc u

60
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(Even/Odd) sec(-u)

sec u

61
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(Even/Odd) cot(-u)

-cot u

62
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(Sum/Difference) sin(u+v)

sin ucos v+cos usin v

63
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(Sum/Difference) sin(u-v)

sin ucos v-cos usin v

64
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(Sum/Difference) cos(u+v)

cos ucos v-sin usin v

65
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(Sum/Difference) cos(u-v)

cos ucos v+sin usin v

66
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(Sum/Difference) tan(u+v)

(tan u+tan v)/(1-tan u*tan v)

67
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(Sum/Difference) tan(u-v)

(tan u-tan v)/(1+tan u*tan v)

68
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(Double Angle) sin 2x

2sin x*cos x

69
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(Double Angle) cos 2x (cos/sin)

cos²x-sin²x

70
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(Double Angle) cos2x (cos)

2cos²x-1

71
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(Double Angle) cos2x (sin)

1-2sin²x

72
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(Double Angle) tan2x

(2tanx)/(1-tan²x)