Trig Identities & other rules to remember

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Last updated 8:20 PM on 7/21/26
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15 Terms

1
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tan(A + B)

(tanA + tanB) / (1 - tanAtanB)

2
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tan(A - B)

(tanA - tanB) / (1 + tanAtanB)

3
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sin(2X)

2sinXcosX

4
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cos(2X)

cos²X - sin²X

5
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tan(2X)

2tanX / (1 - tan²X)

6
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sin(X/2)

±sqrt(1 - cosX) / 2

7
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cos(X/2)

±sqrt(1 + cosX) / 2

8
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tan(X/2)

±sqrt(1 - cosX) / (1 + cosX) or (1 - cosX) / sinX or sinX / (1 + cosX)

9
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sin(3X)

3sinX - 4sin³X

10
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cos(3X)

4cos³X - 3cosX

11
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tan(3X)

(3tanX - tan³X) / (1 - 3tan²X)

12
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a³ + b³

(a + b)(a² - ab + b²)

13
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a³ - b³

(a - b)(a² + ab + b²)

14
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1 + tan²

sec²

15
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1 + cot²

csc²