Home
Class 11
MATHS
If 0 lt x lt 1, then sqrt(1+x^2)[{xcos(c...

If `0 lt x lt 1`, then `sqrt(1+x^2)[{xcos(cos^-1x)+sin(cot^-1x)}^2-1]^(1//2)` =

A

`x/sqrt(1+x^2)`

B

x

C

`xsqrt(1+x^2)`

D

`sqrt(1+x^2)`

Text Solution

Verified by Experts

The correct Answer is:
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

If 0 < x <1, then sqrt(1+x^2)[{xcos(cot^-1x)+sin(cot^-1 x)}^2-1]^(1/2) is equal to

If -1 lt x lt 0 , then cos^(-1) x is equal to

int(xcos^-1x)/sqrt(1-x^2)dx

If 0 lt x lt pi/2 , show that, cos x gt 1-x^(2)/(2!)

If (1)/(sqrt2) lt x lt 1 , then prove that cos^(-1) x + cos^(-1) ((x + sqrt(1 - x^(2)))/(sqrt2)) = (pi)/(4)

If 0 < cos^-1(x) <1 and 1+sin(cos^(-1)x)+sin^2(cos^(-1)x)+sin^3(cos^(-1)x) + ..... =2 then the value of 12 x^2 is____

If pi < x < 2pi, prove that (sqrt(1+cosx)+sqrt(1-cosx))/(sqrt(1+cosx)-sqrt(1-cosx))="cot(x/2+pi/4)dot

The solution set of the equation sin^(-1) sqrt(1 - x^(2)) + cos^(-1) x = cot^(-1) ( sqrt(1-x^(2))/x) - sin^(-1) x

The solution set of the inequation cos^(-1)x lt sin^(-1)x is:

If x lt 0 , the prove that cos^(-1) ((1 + x)/(sqrt(2(1 + x^(2))))) = (pi)/(4) - tan^(-1) x

PATHFINDER-TRIGONOMETRIC EQUATION AND INVERSE-QUESTION BANK
  1. The most general solution of the equation tan^-1(1/2secx)+cot^-1(2cosx...

    Text Solution

    |

  2. The greatest of tan1, tan^-1 1, sin^-1 1, sin1, cos1, is

    Text Solution

    |

  3. If 0 lt x lt 1, then sqrt(1+x^2)[{xcos(cos^-1x)+sin(cot^-1x)}^2-1]^(1/...

    Text Solution

    |

  4. The range of values of a for which the equation sin^2x-sqrt3 sinx cosx...

    Text Solution

    |

  5. The number of points inside or on the circle x^2+y^2=4 satisfying tan^...

    Text Solution

    |

  6. The least difference between the roots in the first quadrant in [0, pi...

    Text Solution

    |

  7. The general solution of the equation sinx-3sin2x+sin3x=cosx-3cos2x+cos...

    Text Solution

    |

  8. General solution of theta satisfying the equation tan^2theta+sec2theta...

    Text Solution

    |

  9. The solution of the inequality log(1//2)sinx gt log(1//2)cosx in [0, 2...

    Text Solution

    |

  10. If [cot^-1x]+[cos^-1x]=0, where x is a non-negative real number and [ ...

    Text Solution

    |

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

    Text Solution

    |

  12. The number of real solutions of tan(5picosalpha)=cot(5pisinalpha), alp...

    Text Solution

    |

  13. If x+y=pi/4 and tanx+tany=1, then

    Text Solution

    |

  14. The number of solution of the equation 2tanx+x=(12pi)/5 in the interva...

    Text Solution

    |

  15. The value of cos^-1(cos5) is

    Text Solution

    |

  16. If x1, x2, x3, x4 are roots of the equation x^4-x^3sin2beta+x^2cos2bet...

    Text Solution

    |

  17. If x+1/x=2, the principle value ot sin^-1x is

    Text Solution

    |

  18. If cos^-1x+cos^-1y+cos^-1z=3pi, then xy+yz+zx is equal to

    Text Solution

    |

  19. If 1-tanx/1+tanx=tany and x-y=pi/6, then x, y are respectively

    Text Solution

    |

  20. If cos^4x+4sin^4x=1, then general value of x equals to

    Text Solution

    |