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The least and the greatest values of `(sin^(-1)x)^3+(cos^(-1)x)^3` are `(-pi)/2,pi/2` (b) `(-pi^3)/8,(pi^3)/8` `(pi^3)/(32),(7pi^3)/8` (d) none of these

A

`-(pi)/(2),(pi)/(2)`

B

`-(pi^(3))/(8),(pi^(3))/(8)`

C

`(pi^(3))/(32),(7 pi^(3))/(8)`

D

none of these

Text Solution

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The correct Answer is:
C
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OBJECTIVE RD SHARMA-INVERSE TRIGONOMETRIC FUNCTIONS -Exercise
  1. The value of sin^(-1)[cos((33pi)/5)] is

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  2. Find the smallest and the largest values of tan^(-1) ((1 - x)/(1 + x))...

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  3. The least and the greatest values of (sin^(-1)x)^3+(cos^(-1)x)^3 are (...

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  4. If a le 1/32 then the number of solution of (sin^(-1) x)^(3) +(cos^(...

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  5. If x takes negative permissible vlaue then sin^(-1)x=

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  6. If -1 le x le -(1)/sqrt(2) then sin^(-1)2xsqrt(1-x^(2)) equals

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  7. If (1)/sqrt(2) le x le 1 then sin^(-1) 2xsqrt(1-x^(2)) equals

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  8. If 0 le x le 1 then cos^(-1)(2x^(2)-1) equals

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  9. If -1 le x le 0 then cos^(-1)(2x^(2)-1) equals

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  10. If -1/2 le x le 1/2 then sin^(-1)3x-4x^(3) equals

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  11. If 1/2 le x le 1 then sin^(-1)3x-4x^(3) equals

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  12. If -1 le x le -1/2, then sin^(-1)(3x-4x^3) equals

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  13. If 1/2 le x le 1 then cos^(-1)(4x^(3)-3x) equals

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  14. if -1/2 le x le 1/2 then cos^(-1)(4x^(3)-3x) equals

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  15. if -1 le x le -1/2 then cos^(-1)(4x^(3)-3x) equals

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  16. If 1 lt x lt 1 then tan^(-1) (2x)/(1-x^(2)) equals

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  17. If x in (1,oo) then tan^(-1)(2x)/(1-x^(2)) equals

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  18. if x in (-oo,-1) then tan^(-1)(2x)/(1-x^(2)) equals

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  19. If -(1)/sqrt(3) lt x lt (1)/sqrt(3), then tan^(-1) (3x-x^(3))/(1-3x^(...

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  20. If x gt (1)/sqrt(3) then tan^(-1) (3x-x^(3))/(1-3x^(2)) equals

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