Cancellation Equations for Inverse Functions

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12 Terms

1
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sin(sin^-1 x)

interval [-1,1]

2
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sin^-1 (sin0-)

interval [-pi/2 , pi/2]

3
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cos(cos^-1 x)

interval [-1,1]

4
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cos^-1 (cos0-)

[0,pi]

5
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tan(tan^-1x)

(-infinity, infinity)

6
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tan^-1 (tan0-)

(-pi/2, pi/2)

7
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sec^-1(secx)

[0,pi] except pi/2

8
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sec(sec^-1x)

(-infinity,-1]U[1,infinity)

9
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csc^-1(cscx)

[-pi/2, pi/2] except 0

10
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csc(csc^-1x)

(-infinity,-1]U[1,infinity)

11
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cot^-1(cotx)

(0,pi)

12
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cot(cot^-1x)

(-infinity,infinity)