Home
Class 12
MATHS
Solve for x if (cot^(-1)x)^2-3(cot^(-1)x...

Solve for `x` if `(cot^(-1)x)^2-3(cot^(-1)x)+2>0`

Text Solution

Verified by Experts

`(cot^(-1) x - 1) (cot^(-1) x -2) gt 0` ltrbgt `rArr cot^(-1) x lt 1 " or " cot^(-1) x gt 2`
`rArr gt cot 1 " or " x lt cot2 ( :' cot^(-1) x " is a decrasing function")`
`rArr x lt cot 2 " or " x gt cot 1`
Promotional Banner

Topper's Solved these Questions

  • INTRODUCTION TO VECTORS

    CENGAGE PUBLICATION|Exercise TRUE OR FALSE|1 Videos

  • JEE 2019

    CENGAGE PUBLICATION|Exercise Chapter 10|8 Videos

Similar Questions

Explore conceptually related problems

sin(cot^(-1)x) =

Solve tan^(-1) x gt cot^(-1) x

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

int (e^(cot^(-1)x))/(1+x^(2))dx

The solution set of inequality (cot^(-1)x)(tan^(-1)x)+(2-pi/2)cot^(-1)x-3tan^(-1)x-3(2-pi/2)>0 is (a , b), then the value of cot^(-1)a+cot^(-1)b is____

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

The value of x if tan^(-1)x + 2 cot^(-1)x = (2 pi)/3 is

The value of 2tan^(-1)(cos e ctan^(-1)x-tancot^(-1)x) is equal to (a) cot^(-1)x (b) cot^(-1)1/x (c) tan^(-1)x (d) none of these

Solve cot^(-1) ((3x^(2) + 1)/(x)) = cot^(-1) ((1 - 3x^(2))/(x)) - tan^(-1) 6x

Solve tan^(-1) x + cot^(-1) (-|x|) = 2 tan^(-1) 6x

CENGAGE PUBLICATION-INVERSE TRIGONOMETRIC FUNCTIONS-All Questions
  1. Solve sin^(-1)x > -1

    Text Solution

    |

  2. Solve cos^(-1)x >cos^(-1)x^2

    Text Solution

    |

  3. Solve for x if (cot^(-1)x)^2-3(cot^(-1)x)+2>0

    Text Solution

    |

  4. Find the value of x for which the following expression are defined si...

    Text Solution

    |

  5. If [cot^(-1)x]+[cos^(-1)x]=0 , where [] denotes the greatest integer f...

    Text Solution

    |

  6. Find the value of (i) sin^(-1)(2^x) (ii) cos^(-1)sqrt(x^2-x+1) ...

    Text Solution

    |

  7. Find the range of f(x)=|3tan^(-1)x-cos^(-1)(0)|-cos^(-1)(-1)dot

    Text Solution

    |

  8. Find the value of x for which sec^(-1)xsin^(-1)x=pi/2dot

    Text Solution

    |

  9. If sin^(-1)(x^2+2x+2)+tan^(-1)(x^2-3x-k^2)>pi/2, then find the values ...

    Text Solution

    |

  10. If cos^(-1)lambda+cos^(-1)mu+cos^(-1)gamma=3pi, then find the value of...

    Text Solution

    |

  11. If sin^(-1)x1+sin^(-1)x2++sin^(-1)xnlt==(npi)/2,n in N ,n=2m+1, mgeq1...

    Text Solution

    |

  12. Find x satisfying [tan^(-1)x]+[cot^(-1)x]=2, where [] represents the g...

    Text Solution

    |

  13. If cos(2sin^(-1)x)=1/9, then find the values of xdot

    Text Solution

    |

  14. Find the value of sin((1)/(2) cot^(-1) (-(3)/(4)))

    Text Solution

    |

  15. Prove that: cot^(-1)((sqrt(1+sinx)+sqrt(1-sinx))/(sqrt(1+sinx)-sqrt(1-...

    Text Solution

    |

  16. Solve sin^(-1)(1-x)-2s in^(-1)x=pi/2

    Text Solution

    |

  17. Find the number of solution of the equation "cos"(cos^(-1)x)=cos e c(c...

    Text Solution

    |

  18. Find the principal values of the following (i) sin^(-1) (sin 1) (ii...

    Text Solution

    |

  19. Solve sin^(-1) (sin 6x) = x, x in [0,pi]

    Text Solution

    |

  20. Solve sin^(-1)[((2x^2+4)/(1+x^2))]<pi-3

    Text Solution

    |