Home
Class 12
MATHS
If x, y, z are all non zero and x^(2)+y^...

If `x, y, z` are all non zero and `x^(2)+y^(2)+z^(2)=r^(2)` then `tan ^(-1)((y z)/(x r))+tan ^(-1)((z x)/(y r))+tan ^(-1)((x y)/(z r))`

A

`(pi)/(4)`

B

`pi`

C

`(pi)/(2)`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • INDEFINITE INTEGRAL

    HIMALAYA PUBLICATION|Exercise QUESTION BANK|404 Videos

  • LIMITS, CONTINUITY AND DIFFERENTIABILITY

    HIMALAYA PUBLICATION|Exercise QUESTION BANK|354 Videos

Similar Questions

Explore conceptually related problems

If x^2+y^2+z^2=r^2,t h e ntan^(-1)((x y)/(z r))+tan^(-1)((y z)/(x r))+tan^(-1)((x z)/(y r)) is equal to

tan ^(-1)((1)/(x+y))+tan ^(-1)((y)/(x^(2)+x y+1))=

If tan ^(-1) x+tan ^(-1) y+tan ^(-1) z=(pi)/(2), then 1-x y-y z-z x=

If tan ^(-1) x+tan ^(-1) y+tan ^(-1) z=(pi)/(2) then x y+y z+z x=

If x,y,z are in A.P. and tan^(-1)x , tan^(-1)y and tan^(-1) z are also in A.P., then :

If x,y,z are in A.P. and tan^(-1) x , tan^(-1) y and tan^(-1) z are also in A.P. then :

If z^(2)+z+1=0 then sum_(r=1)^(6)(z^(r)+(1)/(z^(r)))^(2)=

Verify that x ^(3) + y ^(3) + z ^(3) - 3xyz =1/2 (x + y + z) [(x-y)^(2) + (y-z) ^(2) + (z-x) ^(2) ]

If x,y,z be three positive numbers such that xyz^(2) has the greatest value (1)/(64) , then the value of (1)/(x)+(1)/(y)+(1)/(z) is

If x, y, z are all different and not equal to zero and |{:(1+x,,1,,1),(1,,1+y,,1),(1,,1,,1+z):}| = 0 then the value of x^(-1) + y^(-1) + z^(-1) is equal to

HIMALAYA PUBLICATION-INVERSE TRIGONOMETRIC FUNCTIONS-QUESTION BANK
  1. The solution of tan^(-1)x + 2 cot^(-1)x = (2pi)/(3) is

    Text Solution

    |

  2. The sum of tan ^(-1) (1)/(2)+tan ^(-1) (1)/(8)+tan ^(-1) (1)/(18)+.. i...

    Text Solution

    |

  3. If x, y, z are all non zero and x^(2)+y^(2)+z^(2)=r^(2) then tan ^(-1)...

    Text Solution

    |

  4. "tan"1/2["sin"^(-1)(2x)/(1+x^(2))+"cos"^(-1)(1-y^(2))/(1+y^(2))]

    Text Solution

    |

  5. cot^(-1)(sqrt(cosalpha))-tan^(-1)(sqrt(cosalpha))=x, then sin x =

    Text Solution

    |

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

    Text Solution

    |

  7. Ifcos^(-1) x - cos ^(-1) (y)/(2) =alpha then 4x^(2) -4xy cos alpha+ ...

    Text Solution

    |

  8. If sin^(-1)(x)/(5)+cosec^(-1)(5)/(4)=(pi)/(2)then x=

    Text Solution

    |

  9. If x=sin^(-1) k, y=cos^(-1) k, -1 le k le 1, then the correct relation...

    Text Solution

    |

  10. If tan (cos ^(-1) x)=

    Text Solution

    |

  11. sin ^(-1) x=(pi)/(5), then cos ^(-1) x=

    Text Solution

    |

  12. If tan (cos ^(-1) x)=

    Text Solution

    |

  13. If sin^(-1) (x - (x^(2))/(2 ) + (x^(3))/(4)….)+cos^(-1)(x^2-x^4/2+x^6/...

    Text Solution

    |

  14. 3 sin ^(-1)((2 x)/(1+x^(2)))-4 cos ^(-1)((1-x^(2))/(1+x^(2))) +2 tan ...

    Text Solution

    |

  15. If tan ^(-1)(x+1)+tan ^(-1)(x-1)=tan ^(-1) (8)/(31) then x=

    Text Solution

    |

  16. If cos ^(-1)((3)/(5))-sin ^(-1)((4)/(5))=cos ^(-1) x, then x=

    Text Solution

    |

  17. tan ((1)/(2) cos ^(-1) 0)=

    Text Solution

    |

  18. If tan ^(-1) x+tan ^(-1) y+tan ^(-1) z=(pi)/(2), then 1-x y-y z-z x=

    Text Solution

    |

  19. The value of (tan^(-1) ((1)/(2)) + tan^(-1) ((1)/(3)))=

    Text Solution

    |

  20. If tan^(-1)3+tan^(-1)x=tan^(-1)8, then x=

    Text Solution

    |