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√(a² + x²)
- x = a tan θ
- 1 + tan² θ = sec² θ, -½ π < θ < ½ π
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√(a² - x²)
- x = a sin θ
- 1 - sin² θ = cos² θ, -½ π < θ < ½ π
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√(x² - a²)
- x = a sec θ
- sec² θ - 1 = tan² θ, 0 < θ < 3π/2
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(1) cos 2x
cos² x - sin² x
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tan 2x
2 tan x / (1 - tan² x)
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d/dx arcsin x
1 / √(1 - x²)
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d/dx arccos x
-1 / √(1 - x²)
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d/dx arctan x
1 / (1 + x²)
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d/dx arccsc x
-1 / x√(x² - 1)
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d/dx arcsec x
1 / x√(x² - 1)
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d/dx arccot x
-1 / (1 + x²)
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cos odd
factor cos x ; cos² x = 1 - sin² x ; u = sin x
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sin odd
factor sin x ; sin² x = 1 - cos² x ; u = cos x
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sin, cos even
half-angle identities ; sometimes use sin x cos x = sin 2x / 2
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sec even
factor sec² x ; sec² x = 1 + tan² x ; u = tan x
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tan odd
factor sec x tan x ; tan² x = sec² x - 1 ; u = sec x
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tan even, sec odd
express all as sec
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