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54 lines
1.1 KiB
Markdown
54 lines
1.1 KiB
Markdown
---
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cards-deck: default_obsidian
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---
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#math/calculus
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#math/calculus
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# trig identity
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## basic
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$sin^2x$ ::: $sin^2x+cos^2x=1$ ^1651675101678
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$sin^2x$ halves ::: $sin^2x=1/2(1-cos{2x})$ ^1651675101686
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$cos^2x$ ::: $\cos^2x=1/2(1+\cos{2x})$ ^1651674952732
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$\sin x\cos x$ ::: $=\frac{1}{2}sin2x$ ^1651675101693
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## $tan^{2}x + 1$
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#card/reverse
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$tan^{2}x + 1 = sec^{2}x$
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because: $\frac{sin^{2}x}{cos^{2}x} + \frac{cos^{2}x}{cos^{2}x} = \frac{1}{cos^{2}x}$
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^1651675939328
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## derivatives
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$\frac{dx}{dy}\sec x$ ::: $\tan x \sec x$ ^1651677169665
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$\frac{dx}{dy}\tan x$ ::: $\sec^{2}x$ ^1651679351621
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$\frac{d x}{d y} \ln |x|$ ::: $\frac{1}{x}$ ^1652457023180
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## integrals
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$\int \sec x dx$ ::: $\ln |\sec x + \tan x|$ ^1651679351627
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$\int \tan x dx$ ::: $\ln |\cos x|+C$ ^1652457023184
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## crazy identities
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$\sin A \cos B$ ::: $\frac{1}{2}(\sin(A-B)+\sin(A+B))$ ^1651679351632
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$\sin A \sin B$ ::: $\frac{1}{2}(\cos(A-B)-\cos(A+B))$ ^1651679351636
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$\cos A \cos B$ ::: $\frac{1}{2}(\cos(A-B)+\cos(A+B))$ ^1651679351639
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$\csc^{2}x=$ ::: $=1+\cot^{2}x$ ^1652457023188
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