Home
Class 12
MATHS
The number of real solution of the equat...

The number of real solution of the equation `tan^(-1) sqrt(x^2-3x +2) + cos^(-1) sqrt(4x-x^2 - 3) = pi` is

A

one

B

two

C

zero

D

infinite

Text Solution

Verified by Experts

The correct Answer is:
C
Since `sqrt(x^(2) - 3x + 2) ge 0`
`rArr 0 le tan^(-1) sqrt(x^(2) - 3x + 2) lt (pi)/(2)`
and `sqrt(4x -x^(2) -3) le 0 rArr 0 lt cos^(-1) sqrt(4x - x^(2) -3) le (pi)/(2)`
Adding, we have `0 lt L.H.S. lt pi`
Therefore, the given equation has no solution
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

The number of real solutions of the equation 2sin^-1sqrt((x^2-x+1))+cos^-1sqrt((x^2-x))=(3pi)/2

The number of solution of the equation tan^-1 sqrt(x(x+1)) + sin^-1sqrt(x^2 + x + 1) = pi/2

Find the number of real solutions to the equation 3cos^(-1)x-pix-pi/2=0

The sum of the solution of the equation 2sin^(-1)sqrt(x^2+x+1)+cos^(-1)sqrt(x^2+x)=(3pi)/2 is 0 (b) -1 (c) 1 (d) 2

The number of solutions of the equation sin((pix)/(2sqrt3))=x^2-2sqrt3x+4 is

The number of solution(s) of the equation sqrt(x+1)-sqrt(x-1)=sqrt(4x-1) is/are

The number of solutions of the equation sqrt(x^(2))-sqrt((x-1)^(2))+sqrt((x-2)^(2))=sqrt(5) is

The number of solutions (s) of the equation sqrt(x+1)-sqrt(x+1)=sqrt(4x+1) is /are -

Find the number of real solutions of the equation sqrt(1 + cos 2x) = sqrt2 cos^-1 (cosx) , where x in [pi/2 , pi]

Solve: tan^(-1)sqrt(x(x+1) + sin^(-1)sqrt(1+x+x^2) = pi/2

CENGAGE PUBLICATION-INVERSE TRIGONOMETRIC FUNCTIONS-All Questions
  1. The maximum value of f(x)=tan^(-1)(((sqrt(12)-2)x^2)/(x^4+2x^2+3)) is...

    Text Solution

    |

  2. For the equation cos^(-1)x+cos^(-1)2x+pi=0 , the number of real soluti...

    Text Solution

    |

  3. The number of real solution of the equation tan^(-1) sqrt(x^2-3x +2) +...

    Text Solution

    |

  4. If sin^(-1)(x-1)+cos^(-1)(x-3)+tan^(-1)(x/(2-x^2))=cos^(-1)k+pi, then ...

    Text Solution

    |

  5. Find the number of real solutions to the equation sqrt(1+cos2x)=sqrt2 ...

    Text Solution

    |

  6. The equation 3 cos^(-1) x - pi x - (pi)/(2) =0has

    Text Solution

    |

  7. Range of f(x)=sin^(-1)x+tan^(-1)x+sec^(-1)x is (pi/4,(3pi)/4) (b) [pi...

    Text Solution

    |

  8. The value of underset( |x| -> infty) lim cos( tan^(-1)(sin(tan^(-1)x))...

    Text Solution

    |

  9. Find the range of tan^(-1)((2x)/(1+x^2))

    Text Solution

    |

  10. Complete solution set of (cot^(-1)x)+2(tan^(-1)x)=0, where [] denotes ...

    Text Solution

    |

  11. The number of integral values of k for which the equation sin^(-1)x+ta...

    Text Solution

    |

  12. The range of value of p for which the equation sincos^(-1)("cos"(tan^(...

    Text Solution

    |

  13. The number of real solutions of the equation 2sin^-1sqrt((x^2-x+1))+co...

    Text Solution

    |

  14. Complete solution set of tan^2(sin^(-1)x)>1 is (-1,-1/(sqrt(2)))uu(1/(...

    Text Solution

    |

  15. The trigonometric equation sin^(-1)x=2sin^(-1)a has a solution for all...

    Text Solution

    |

  16. The number of solution of equation sin^(-1)x+nsin^(-1)(1-x)=(mpi)/2,wh...

    Text Solution

    |

  17. If |cos^(-1)((1-x^2)/(1+x^2))| < pi/3,t h e n (a) x in [-1/3,1/(sqrt(...

    Text Solution

    |

  18. The value of sin^(-1)(sin12)+cos^(-1)(cos12)=

    Text Solution

    |

  19. The value of the expression sin^(-1)(sin(22pi)/7)+cos^(-1)(cos(5pi)/3)...

    Text Solution

    |

  20. The value of sin^(-1)("cos"(cos^(-1)(cosx)+sin^(-1)(sinx))), where x i...

    Text Solution

    |