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Find the range of y = (cot^(-1) x) (cot^...

Find the range of `y = (cot^(-1) x) (cot^(-1) (-x))`

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To find the range of the function \( y = \cot^{-1}(x) \cdot \cot^{-1}(-x) \), we can follow these steps: ### Step 1: Rewrite \( \cot^{-1}(-x) \) We know that: \[ \cot^{-1}(-x) = \pi - \cot^{-1}(x) \] Thus, we can rewrite the function as: ...
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CENGAGE ENGLISH-INVERSE TRIGONOMETRIC FUNCTIONS-Illustration
  1. Find the value of sin^(-1) (sin 5) + cos^(-1) (cos 10) + tan^(-1) {tan...

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  2. Find the minimum value of the function f(x) = (pi^(2))/(16 cot^(-1) (-...

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  3. Find the range of y = (cot^(-1) x) (cot^(-1) (-x))

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  4. The value of 2 tan^(-1) (cosec tan^(-1) x - tan cot^(-1) x) is equal t...

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  5. Prove that cos (tan^(-1) (sin (cot^(-1) x))) = sqrt((x^(2) + 1)/(x^(2)...

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  6. If sin^(-1) x = pi//5, for some x in (-1, 1), then find the value of c...

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  7. If sin (sin^(-1).(1)/(5) + cos^(-1) x) = 1, then find the value of x

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  8. solve sin^(-1) x le cos^(-1) x

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  9. Find the range of f(x) = sin^(-1) x + tan^(-1) x + cos^(-1) x

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  10. Find the minimum value of (sec^(-1) x)^(2) + (cosec^(-1) x)^(2)

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  11. Find the range of f(x) = (sin^(-1) x)^(2) + 2pi cos^(-1) x + pi^(2)

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  12. Solve sin^(-1). (14)/(|x|) + sin^(-1).(2 sqrt15)/(|x|) = (pi)/(2)

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  13. If alpha = sin^(-1) (cos(sin^-1) x)) and beta = cos^(-1) (sin (cos^(-1...

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  14. If sec^(-1) x = cosec^(-1) y, then find the value of cos^(-1).(1)/(x) ...

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  15. Prove that tan^(-1) x + tan^(-1).(1)/(x) = {(pi//2,"if" x gt 0),(-pi//...

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  16. For which values of x, function f(x) = sin^(-1) x + sin^(-1).(1)/(x) +...

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  17. Find the value of sum(r = 1)^(10) sum(s = 1)^(10) tan^(-1) ((r)/(s))

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  18. If sin^(-1)xi in [0,1]AAi=1,2,3, .28 then find the maximum value of s...

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  19. If two angles of a triangle are tan^(-1) (2) and tan^(-1) (3), then fi...

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  20. Prove that cos^(-1).(4).(5) + cos^(-1).(12)/(13) = cos^(-1).(33)/(65)

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