Trig identities

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Last updated 1:12 PM on 1/15/26
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20 Terms

1
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sin(α ± β) =

= sinα*cosβ

2
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cos(α ± β) =

= cosα*cosβ

3
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tan(α ± β) =

= tanα ± tanβ/1 ∓ tanα*tanβ

4
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csc(α ± β) =

= secα secβ cscα cscβ/secα cscβ ± cscα secβ

5
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sec(α ± β) =

= secα secβ cscα cscβ/cscα cscβ ∓ secα secβ

6
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cot(α ± β) =

= cotα cotβ ∓ 1/cotβ ∓ cotα

7
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sin(2θ) =

= 2sinθcosθ

8
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cos(2θ) =

= cos(θ)2 - sin(θ)2

9
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csc(x) =

1/sin(x) =

10
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sec(x) =

1/cos(x) =

11
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cot(x) =

1/tan(x)

12
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sec2(x) =

1 + tan2(x) =

13
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csc2(x) =

1 + cot2(x) =

14
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sin(x/2) =

±√(1 - cos(x)/2)

15
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cos(x/2) =

±√(1+cos(x)/2)

16
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tan(x/2) =

1 - cos(x)/sin(x) =

17
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sin(a+b) =

sin(a)cos(b) + cos(a)sin(b) =

18
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sin(a-b) =

sin(a)cos(b) - cos(a)sin(b) =

19
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cos(a+b) =

cos(a)cos(b) - sin(a)sin(b) =

20
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cos(a-b) =

cos(a)cos(b) + sin(a)sin(b) =