Home
Class 11
MATHS
The greatest and least values of (sin^-1...

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

A

`pi^3/(32)`

B

`-pi^3/8`

C

`(7pi^3)/8`

D

`pi/2`

Text Solution

Verified by Experts

The correct Answer is:
A, C
Promotional Banner

Topper's Solved these Questions

  • TRIGONOMETRIC EQUATION

    PATHFINDER|Exercise QUESTION BANK|21 Videos
  • TRIGONOMETRIC FUNCTIONS

    PATHFINDER|Exercise QUESTION BANK|68 Videos

Similar Questions

Explore conceptually related problems

The greatest and least values of f(x)=tan^(-1)x -(1)/(2) ln x on [(1)/(sqrt(3)),sqrt(3)] are

IF x is real , find the greatest and the least value of : (x^2-2x+2)/(x^2+3x+9)

IF x is real , find the greatest and the least value of : (x^2+14x+9)/(x^2+2x+3)

The difference between the greatest and least values of the function f(x)=cosx+1/2cos2x-1/3cos3x , is

Solve for real values of x :((sin^(-1)x)^3+(cos^(-1)x)^3)/((tan^(-1)x+cot^(-1)x)^3)=7

The least value of (1+sec^(-1)x)(1+cos^(-1)x) is ________

The value of sin(cos^(-1)x)-cos(sin^(-1)x) is

The value of sin(cos^(-1)x)-cos(sin^(-1)x) is-

Find the set of values of parameter a so that the equation (sin^(-1)x)^3+(cos^(-1)x)^3=api^3 has a solution.

The set of values of x satisfying abs(sin^-1x) lt abs(cos^-1x) , is

PATHFINDER-TRIGONOMETRIC EQUATION AND INVERSE-QUESTION BANK
  1. The solution of the equation sin[2cos^-1{cot(2tan^-1x)}] = 0 are

    Text Solution

    |

  2. Let f(x)=e^(cos^-1sin(x+pi/3)), then

    Text Solution

    |

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

    Text Solution

    |

  4. alpha is a root of the equation (2sinx-cosx)(1+cosx)=sin^2x beta is a...

    Text Solution

    |

  5. alpha is a root of the equation (2sinx-cosx)(1+cosx)=sin^2x beta is a...

    Text Solution

    |

  6. f(x)=sin{cot^-1(x+1)}-cos(tan^-1x) a=costan^-1sincot^-1x b=cos(2cos^-1...

    Text Solution

    |

  7. f(x)=sin{cot^-1(x+1)}-cos(tan^-1x) a=costan^-1sincot^-1x b=cos(2cos^-1...

    Text Solution

    |

  8. sum(r=1)^ntan^-1((xr-x(r-1))/(1+x(r-1)xr))=sum(r=1)^n(tan^-1xr-tan^-1x...

    Text Solution

    |

  9. sum(r=1)^ntan^-1((xr-x(r-1))/(1+x(r-1)xr))=sum(r=1)^n(tan^-1xr-tan^-1x...

    Text Solution

    |

  10. Arrange the followig radicals in increasing order of -I effect. 1,Br,C...

    Text Solution

    |

  11. Match Column-I with Column-II

    Text Solution

    |

  12. The number of values of theta in the interval (-pi/2, pi/2) such that ...

    Text Solution

    |

  13. If a, b, c, d in (0, pi) and b+c ne pi/2 such that 2cosa+6cosb+7cosc+9...

    Text Solution

    |

  14. The value of 1/2{sec^2(tan^-1 2)+cosec^2(cot^-1 3)+tan^2(pi/3)} is equ...

    Text Solution

    |

  15. If x gt 0, then the value of sin{tan^-1((1-x^2)/(2x))+cos^-1((1-x^2)/(...

    Text Solution

    |

  16. If cos^-1(x/2)+sin^-1(x/4)=pi/6, then the value of x is

    Text Solution

    |

  17. Solve: cos^4(x/5)+sin^2(x/5)=1

    Text Solution

    |

  18. Solve: abscot(2x-pi/2)=1/(cos^2 2x)-1

    Text Solution

    |

  19. Solve: 2cos^2x+5cosx+2 ge 0

    Text Solution

    |

  20. Find the points of intersection of the curves y=cosx and y=sin3x if -p...

    Text Solution

    |