Math Trigonometric Identities
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Last updated 10:13 PM on 2/3/25
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50 Terms
1
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sin θ
1/csc θ
2
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cos θ
1/sec θ
3
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tan θ
1/cot θ
4
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csc θ
1/sin θ
5
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sec θ
1/cos θ
6
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cot θ
1/tan θ
7
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tan θ
sin θ / cos θ
8
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cot θ
cos θ / sin θ
9
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sin² θ + cos² θ
1
10
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tan² θ + 1
sec² θ
11
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cot² θ + 1
csc² θ
12
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sin θ
cos(π/2 - θ)
13
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csc θ
sec(π/2 - θ)
14
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cos θ
sin(π/2 - θ)
15
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sec θ
csc(π/2 - θ)
16
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tan θ
cot(π/2 - θ)
17
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cot θ
tan(π/2 - θ)
18
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sin(-θ)
-sin θ
19
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csc(-θ)
-csc θ
20
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cos(-θ)
cos θ
21
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sec(-θ)
sec θ
22
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tan(-θ)
-tan θ
23
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cot(-θ)
-cot θ
24
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sin(A + B)
sin A * cos B + cos A * sin B
25
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cos(A + B)
cos A * cos B - sin A * sin B
26
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tan(A + B)
(tan A + tan B) / (1 - tan A * tan B)
27
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sin(A - B)
sin A * cos B - cos A * sin B
28
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cos(A - B)
cos A * cos B + sin A * sin B
29
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tan(A - B)
(tan A - tan B) / (1 + tan A * tan B)
30
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sin 2θ
2 sin θ * cos θ
31
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cos 2θ
cos² θ - sin² θ
32
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cos 2θ
1 - 2 sin² θ
33
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cos 2θ
2 cos² θ - 1
34
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tan 2θ
(2 tan θ) / (1 - tan² θ)
35
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sin (θ/2)
±√((1 - cos θ) / 2)
36
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cos (θ/2)
±√((1 + cos θ) / 2)
37
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tan (θ/2)
±√((1 - cos θ) / (1 + cos θ))
38
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tan (θ/2)
(1 - cos θ) / sin θ
39
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tan (θ/2)
sin θ / (1 + cos θ)
40
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sin² θ
(1 - cos 2θ) / 2
41
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cos² θ
(1 + cos 2θ) / 2
42
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tan² θ
(1 - cos 2θ) / (1 + cos 2θ)
43
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sin A * sin B
(1/2)[cos(A - B) - cos(A + B)]
44
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cos A * cos B
(1/2)[cos(A - B) + cos(A + B)]
45
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sin A * cos B
(1/2)[sin(A + B) + sin(A - B)]
46
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cos A * sin B
(1/2)[sin(A + B) - sin(A - B)]
47
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sin A + sin B
2 sin((A + B) / 2) * cos((A - B) / 2)
48
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cos A + cos B
2 cos((A + B) / 2) * cos((A - B) / 2)
49
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sin A - sin B
2 cos((A + B) / 2) * sin((A - B) / 2)
50
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cos A - cos B
-2 sin((A + B) / 2) * sin((A - B) / 2)
Note 
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