Trig identities

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Last updated 11:04 PM on 7/26/26
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12 Terms

1
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cos(α − β)

cos(α)cos(β) + sin(α)sin(β)

2
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sin(α − β)

sin(α)cos(β) − sin(β)cos(α)

3
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tan(α − β)

tan(α)−tan(β)1+tan(α)tan(β)\frac{tan(\alpha)-tan(\beta)}{1+tan(\alpha)tan(\beta)}

4
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cos(α + β)

cos(α)cos(β) − sin(α)sin(β)

5
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sin(α + β)

sin(α)cos(β) + cos(α)sin(β)

6
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tan(α + β)

tan(α)+tan(β)1−tan(α)tan(β)\frac{tan(\alpha) + tan(\beta)}{1 - tan(\alpha)tan(\beta)}

7
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sin(2θ)

2sin(θ)cos(θ)

8
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cos(2θ)

cos²(θ) − sin²(θ)

OR

2cos²(θ) − 1

OR

1 − 2sin²(θ)

9
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tan(2θ)

2tan(θ) / [1 − tan²(θ)]

OR

±√[(1 − cos(θ)) / (1 + cos(θ))]

OR

[1 − cos(θ)] / sin(θ)

OR

sin(θ) / [1 + cos(θ)]

10
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sin(θ/2)

±√[(1 − cos(θ)) / 2]

11
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cos(θ/2)

±√[(1 + cos(θ)) / 2]

12
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tan(θ/2)

±√[(1 − cos(θ)) / (1 + cos(θ))]

OR

[1 − cos(θ)] / sin(θ)

OR

sin(θ) / [1 + cos(θ)]