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

If `cos^(-1) x + cos^(-1) y + cos^(-1) z = pi ` , then

A

`x^(2) + y^(2) + z^(2) + 2xyz = 1`

B

`2(sin^(-1) x + sin^(-1)y + sin^(-1)z) = cos^(-1) x + cos^(-1) y + cos^(-1) z `

C

` xy + yz + zx = x + y + z - 1`

D

`( x + 1/x) + ( y + 1/y) + ( z+ 1/z) ge 6`

Text Solution

Verified by Experts

The correct Answer is:
A, B
Promotional Banner

Topper's Solved these Questions

  • INVERSE TRIGONOMETRIC FUNCTIONS

    ARIHANT MATHS|Exercise Exercise (Statement I And Ii Type Questions)|14 Videos

  • INVERSE TRIGONOMETRIC FUNCTIONS

    ARIHANT MATHS|Exercise Exercise (Passage Based Questions)|15 Videos

  • INVERSE TRIGONOMETRIC FUNCTIONS

    ARIHANT MATHS|Exercise Exercise (Single Option Correct Type Questions)|70 Videos

  • INDEFINITE INTEGRAL

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|8 Videos

  • LIMITS

    ARIHANT MATHS|Exercise Exercise For Session 6|4 Videos

Similar Questions

Explore conceptually related problems

If cos^(-1) x + cos^(-1) y + cos^(-1) z = pi" , prove that " x^(2) + y^(2)+ z^(2) + 2xyz = 1 .

If cos^(-1)x + cos^(-1)y - cos^(-1) z = 0 , then show that x^(2) + y^(2) + z^(2) - 2xyz = 1

If (i) cos^(-1) x + cos^(-1) y + cos^(-1) z = pi , prove that : x^(2) +y^(2) +z^(2) + 2xyz = 1 (ii) If sin^(-1) x + sin^(-1) y + sin^(-1) z = pi/2 , prove that : x^(2) +y^(2) +z^(2) +2xyz = 1

If cos^(-1)x +cos^(-1)y +cos^(-1)z =3pi then x+y+z is :

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

If cos^(-1)x+cos^(-1)y+cos^(-1)z+cos^(-1)t=4pi , then x^(2)+y^(2)+z^(2)+t^(2)=

If : cos^(-1)x+cos^(-1)y+cos^(-1)z=3pi, " then :" x (y+z)+y(z+x)+z(x+y)=

If cos^(-1)x+cos^(-1)y+cos^(-1)z=3pi ,then the value of x^(2012),+y^(2012)+z^(2012)+(6)/(x^(2011)+y^(2011)+z^(2011)) is equal to:

ARIHANT MATHS-INVERSE TRIGONOMETRIC FUNCTIONS-Exercise (More Than One Correct Option Type Questions)
  1. Let theta = tan^(-1) ( tan . (5pi)/4) " and " phi = tan^(-1) ( - tan ...

    Text Solution

    |

  2. let f(x)=e^(cos^(-1)sin(x + pi/3)) then f((8pi)/9) and f((-7pi)/4)

    Text Solution

    |

  3. If the numerical value of tan{cos^-1(4/5)+tan^-1(2/3)} is a/bthen

    Text Solution

    |

  4. Let f(x) = sin^(-1) x + cos^(-1) x ". Then " pi/2 is equal to

    Text Solution

    |

  5. cos^(-1)x=tan^(-1)x then

    Text Solution

    |

  6. The value(s) of x satisfying the equation sin^-1|sin x|=sqrt(sin^-1|s...

    Text Solution

    |

  7. If (sin^(-1)x+sin^(-1)w)(sin^(-1)y+sin^(-1)z)=pi^2, then D=|x^(N1)y^(N...

    Text Solution

    |

  8. Indicate the relation which can hold in their respective domain for in...

    Text Solution

    |

  9. To the equation 2^2pi//cos^((-1)x)-(a+1/2)2^pi//cos^((-1)x)-a^2=0 has ...

    Text Solution

    |

  10. sin^(-1)(sin 3) + sin^(-1) ( sin 4) + sin^(-1) ( sin 5) when simplif...

    Text Solution

    |

  11. If cos^(-1) x + cos^(-1) y + cos^(-1) z = pi , then

    Text Solution

    |

  12. 2 tan ( tan^(-1)(x)+ tan^(-1)(x^(3))) " where " x in R - {-1,1} is equ...

    Text Solution

    |

  13. Let f(x) = sin^(-1)|sin x| + cos^(-1)( cos x) . Which of the following...

    Text Solution

    |

  14. If f(x) = sin^(-1) x. cos^(-1) x. tan^(-1) x . cot^(-1) x. sec^(-1) x....

    Text Solution

    |

  15. Let alpha = 3 cos^(-1) (5/sqrt28) + 3 tan^(-1) ( sqrt3/2) " and " beta...

    Text Solution

    |

  16. Let function f(x) be defined as f(x) = |sin^(-1)x| + cos^(-1) (1/x)...

    Text Solution

    |

  17. Which of the following pairs of function are identical?

    Text Solution

    |

  18. The value of Sigma(n=1)^(infty) cot^(-1) ( n^(2) + n +1) is also equa...

    Text Solution

    |

  19. Let f : I - {-1,0,1} to [-pi, pi] be defined as f(x) = 2 tan^(-1) x - ...

    Text Solution

    |

  20. If log x = (-1)/3 log y = 2/5 " and " P =log ( sin ( arc cos sqrt(1 - ...

    Text Solution

    |