Home
Class 12
MATHS
If cos e c^(-1)x+cos e c^(-1)y+cos e c^(...

If `cos e c^(-1)x+cos e c^(-1)y+cos e c^(-1)z=-(3pi)/2,` find the value of `x/y+y/z+z/xdot`

A

1

B

`-3`

C

3

D

`3/2`

Text Solution

Verified by Experts

We know that the minimum value of `cosec^(-1)x is -(pi)/(2)` which is attained at x=-1
`therefore cosec^(-1)+cosec^(-1)y+cosec^(-1)z=-(3pi)/(2)`
`rarr cos^(-1)x+cosec^(-1)+cosec^(-1)z=(-pi)/(2)+(-pi)/(2)+(pi)/(2)`
`rarr x=-1,y=-1z=-1`
`therefore x/y+y/z+z/x=(-1)/(-1)+(-1)/(-1)+(-1)/(-1)=3`
Promotional Banner

Topper's Solved these Questions

  • INVERSE TRIGONOMETRIC FUNCTIONS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Section I - Solved Mcqs|71 Videos

  • INVERSE TRIGONOMETRIC FUNCTIONS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Section II - Assertion Reason Type|11 Videos

  • INDEFINITE INTEGRALS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|30 Videos

  • LIMITS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|58 Videos

Similar Questions

Explore conceptually related problems

If "c o s e c"^(-1)x+"c o s e c"^(-1)y+"c o s e c"^(-1)z=-(3pi)/2 , find the value of x/y+y/z+z/x .

If sin^(-1)x+sin^(-1)y+sin^(-1)z=(3pi)/2, find the value of x^2+y^2+z^2

If x , y , z in [-1,1] such that sin^(-1)x+sin^(-1)y+sin^(-1)z=-(3pi)/2, find the value of x^2+y^2+z^2dot

If x , y , z in [-1,1] such that sin^(-1)x+sin^(-1)y+sin^(-1)z=-(3pi)/2, find the value of x^2+y^2+z^2dot

If sec^(-1)x=cos e c^(-1)y , then find the value of cos^(-1)1/x+cos^(-1)1/ydot

If x , y ,z in [-1,1] such that cos^(-1)x+cos^1y+cos^(-1)z=3pi, then find the values of (1) x y+y z+z x and (2) x(y+z)+y(z+x)+z(x+y)

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

If sin^-1x+sin^-1y+sin^-1z=(3pi)/2 , then find the value of x^2+y^2+z^2

If sin^(-1)x+sin^(-1)y=pi/3 and cos^(-1)x-cos^(-1)y=pi/6 , find the values of x and y .

If cos^(-1)x + cos^(-1)y + cos^(-1)z = pi, then xy + yz +zx is equal to

OBJECTIVE RD SHARMA ENGLISH-INVERSE TRIGONOMETRIC FUNCTIONS -Chapter Test
  1. If cos e c^(-1)x+cos e c^(-1)y+cos e c^(-1)z=-(3pi)/2, find the value ...

    Text Solution

    |

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

    Text Solution

    |

  3. If (tan^(-1)x)^2+(cot^(-1)x)^2=(5pi^2)/8, then find xdot

    Text Solution

    |

  4. If tantheta + tan(theta + pi/3) + tan(theta-pi/3)= Ktan3theta, then K ...

    Text Solution

    |

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

    Text Solution

    |

  6. The numerical value of "tan"(2tan^(-1)(1/5)-pi/4 is equal to

    Text Solution

    |

  7. If tan(x+y)=33, and x= tan^(-1)3, then: y=

    Text Solution

    |

  8. Two angles of a triangle are cot^-1 2 and cot^-1 3, then the third ang...

    Text Solution

    |

  9. The greater of the two angles A=2tan^(-1)(2sqrt(2)-1) and B=3sin^(-1)(...

    Text Solution

    |

  10. Let a, b and c be positive real numbers. Then prove that tan^(-1) sqrt...

    Text Solution

    |

  11. If sin^(-1)x+sin^(-1)y+sin^(-1)z=(3pi)/(2) the value of x^(100)+y^(10...

    Text Solution

    |

  12. The value of (alpha^(3))/(2) cosec^(2) ((1)/(2) tan^(-1) ((alpha)/(bet...

    Text Solution

    |

  13. If a,b are positive quantitis and if a(1)=(a+b)/(2), b(1)=sqrt(a(1)b) ...

    Text Solution

    |

  14. tan""(2pi)/(5)-tan""(pi)/(15)-sqrt3tan""(2pi)/(5)tan""(pi)/(15) is equ...

    Text Solution

    |

  15. If a(1), a(2), a(3),...., a(n) is an A.P. with common difference d, th...

    Text Solution

    |

  16. If x=sin(2tan^(- 1)2), y=sin(1/2tan^(- 1)(4/3)) , then -

    Text Solution

    |

  17. Which of the following angles is greater? theta1=sin^(-1)+sin^(-1)1/3o...

    Text Solution

    |

  18. The value of cos[1/2 cos^(-1){cos(sin^(-1)((sqrt63)/(8)))}] is

    Text Solution

    |

  19. Solve for x: - tan^(-1)("x"+1)+tan^(-1)("x"-1)=tan^(-1) (8/31)

    Text Solution

    |

  20. If alpha = sin^(-1)(sqrt(3)/2)+sin^(-1)(1/3) , beta =cos ^(-1)(sqrt(3)...

    Text Solution

    |

  21. The sum of the two angles cot^(-1) 3 and cosec^(-1) sqrt(5) is

    Text Solution

    |