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Math Trigonometric Identities

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50 Terms

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