trig for TOL

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Last updated 2:09 PM on 7/2/26
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16 Terms

1
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sin(α+β)

sinαcosβ+cosαsinβ

2
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cos(α+β)

cosαcosβ-sinαsinβ

3
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tan(α+β)

(tanα+tanβ)/(1-tanαtanβ)

4
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sin(2α)

2sinαcosα

5
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cos 2α

cos²α-sin²α o 1-2sin²α

6
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tan 2α

2tanα/(1-tan²α)

7
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sin α/2

(1−cos⁡α)2\sqrt{\frac{\left(1-\cos\alpha\right)}{2}}

8
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cos(α/2)

(1+cos⁡α)2\sqrt{\frac{\left(1+\cos\alpha\right)}{2}}

9
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tan(α/2)

(1−cos⁡α)1+cos⁡α=(sin⁡α)1+cos⁡α=(1−cos⁡α)sin⁡α\sqrt{\frac{\left(1-\cos\alpha\right)}{1+\cos\alpha}}=\frac{\left(\sin\alpha\right)}{1+\cos\alpha}=\frac{\left(1-\cos\alpha\right)}{\sin\alpha}

10
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sin p + sin q

2sin⁡((p+q)2)cos⁡((p−q)2)2\sin\left(\frac{\left(p+q\right)}{2}\right)\cos\left(\frac{\left(p-q\right)}{2}\right)

11
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sin p - sin q

2cos⁡((p+q)2)sin⁡((p−q)2)2\cos\left(\frac{\left(p+q\right)}{2}\right)\sin\left(\frac{\left(p-q\right)}{2}\right)

12
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cos p + cos q

2cos⁡((p+q)2)cos⁡((p−q)2)2\cos\left(\frac{\left(p+q\right)}{2}\right)\cos\left(\frac{\left(p-q\right)}{2}\right)

13
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cos p - cos q

−2sin⁡((p+q)2)sin⁡((p−q)2)-2\sin\left(\frac{\left(p+q\right)}{2}\right)\sin\left(\frac{\left(p-q\right)}{2}\right)

14
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sinαcosβ=

12(sin⁡(α+β)+sin⁡(α−β))\frac12\left(\sin\left(\alpha+\beta\right)+\sin\left(\alpha-\beta\right)\right)

15
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cosαcosβ

12(cos⁡(α+β)+cos⁡(α−β))\frac12\left(\cos\left(\alpha+\beta\right)+\cos\left(\alpha-\beta\right)\right)

16
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sinαsinβ

12(cos⁡(α−β)−cos⁡(α+β))\frac12\left(\cos\left(\alpha-\beta\right)-\cos\left(\alpha+\beta\right)\right)