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1.
1=π1803600rad0.000291rad1^\prime=\dfrac{\pi}{180 \cdot 3600}\,\text{rad}\approx 0.000291\text{rad}
2.
1=π1803600rad0.000005red1^{\prime\prime}=\dfrac{\pi}{180 \cdot 3600}\,\text{rad}\approx0.000005\,\text{red}
3.
sin2α+cos2α=1\sin^2\alpha+\cos^2\alpha=1
4.
tanα=sinαcosα\tan\alpha=\dfrac{\sin\alpha}{\cos\alpha}
5.
cotα=cosαsinα\cot\alpha=\dfrac{\cos\alpha}{\sin\alpha}
6.
tanαcotα=1\tan\alpha\cdot\cot\alpha=1
7.
tan2α=1cos2α1\tan^2\alpha=\dfrac{1}{\cos^2\alpha}-1
8.
Sine of sum of angles
sin(α+β)=sinαcosβ+sinβcosα\sin(\alpha+\beta)=\sin\alpha \, \cos\beta + \sin\beta \, \cos\alpha
9.
sin(αβ)=sinαcosβsinβcosα\sin(\alpha - \beta) = \sin\alpha \, \cos\beta - \sin\beta\,\cos\alpha
10.
cos(α+β)=cosαcosβsinαsinβ\cos(\alpha+\beta)=\cos\alpha\cos\beta-\sin\alpha\sin\beta
11.
cos(αβ)=cosαcosβ+sinαsinβ\cos(\alpha-\beta)=\cos\alpha\cos\beta+\sin\alpha\sin\beta
12.
tan(α+β)=tanα+tanβ1tanαtanβ\tan(\alpha+\beta)=\dfrac{\tan\alpha + \tan\beta}{1-\tan\alpha\tan\beta}
13.
tan(αβ)=tanαtanβ1+tanαtanβ\tan(\alpha-\beta)=\dfrac{\tan\alpha - \tan\beta}{1+\tan\alpha\tan\beta}
14.
cot(α+β)=1tanαtanβtanα+tanβ\cot(\alpha+\beta)=\dfrac{1-\tan\alpha\tan\beta}{\tan\alpha+\tan\beta}
15.
cot(αβ)=1+tanαtanβtanαtanβ\cot(\alpha-\beta)=\dfrac{1+\tan\alpha\tan\beta}{\tan\alpha-\tan\beta}
16.
Difference of fifth powers
a5b5=(ab)(a4+a3b+a2b2+ab3+b4)a^5-b^5=(a-b)(a^4+a^3b+a^2b^2+ab^3+b^4)
17.
Sum of fifth powers
a5+b5=(a+b)(a4a3b+a2b2ab3+b4)a^5+b^5=(a+b)(a^4-a^3b+a^2b^2-ab^3+b^4)
18.
Square of difference
(ab)2=a22ab+b2(a-b)^2=a^2-2ab+b^2
19.
Square of sum
(a+b)2=a2+2ab+b2(a+b)^2=a^2+2ab+b^2
20.
Cube of difference
(ab)3=a33a2b+3ab2b3(a-b)^3=a^3-3a^2b+3ab^2-b^3