Home
Class 12
MATHS
If cos^(-1)x+cos^(-1)y+cos^(-1)z=pi,t h ...

If `cos^(-1)x+cos^(-1)y+cos^(-1)z=pi,t h e n` `x^2+y^2+z^2+x y z=0` `x^2+y^2+z^2+2x y z=0` `x^2+y^2+z^2+x y z=1` `x^2+y^2+z^2+2x y z=1`

Promotional Banner

Topper's Solved these Questions

Similar Questions

Explore conceptually related problems

If cos^(-1)x + cos^(-1)y + cos^(-1)z = pi , then x^(2) + y^(2) + z^(2) + 2xyz is :

If sin^(-1)x +cos^(-1)y +sin^(-1)z=2pi then 2x-z+y is :

If cos^(-1)x+cos^(-1)y+cos^(-1)z=pi, then x^(2)+y^(2)+z^(2)+xyz=0x^(2)+y^(2)+z^(2)+2xyz=0x^(2)+y^(2)+z^(2)+xyz=1x^(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 : 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 = pi" , prove that " x^(2) + y^(2)+ z^(2) + 2xyz = 1 .

If cos^-1x+cos^-1y+cos^-1 z=pi, then (A) x^2+y^2=z^2 (B) x^2+y^2+z^2=0 (C) x^2+y^2+z^2=1 (D) none of these

If cos^(-1)x+cos^(-1)y+cos^(-1)z=pi, where -1<=x,y,z<=1, then find the value of x^(2)+y^(2)+z^(2)+2xyz

If cos^-1 x+cos^-1 y+cos^-1 z=pi and x+y+z= 3/2, then prove that x=y=z

If sin ^ (- 1) x + sin ^ (- 1) y + sin ^ (- 1) z = pi show that, x ^ (4) + y ^ (4) + z ^ (4) + 4x ^ ( 2) y ^ (2) z ^ (2) = 2 (x ^ (2) y ^ (2) + y ^ (2) z ^ (2) + z ^ (2) x ^ (2))

ALLEN-INVERSE TRIGONOMETRIC FUNCTIONS-All Questions
  1. Domain of the explicit from of the function y represented implicity by...

    Text Solution

    |

  2. If cos^(- 1)x-cos^(- 1)(y/2)=alpha then 4x^2-4xycosalpha+y^2=

    Text Solution

    |

  3. If cos^(-1)x+cos^(-1)y+cos^(-1)z=pi,t h e n x^2+y^2+z^2+x y z=0 x^...

    Text Solution

    |

  4. The solution of the inequality (tan^(-1)x)^2-3tan^(-1)x+2geq0 is- a.(-...

    Text Solution

    |

  5. cos^(-1)x = tan^(-1)x, then: a. x^2=((sqrt(5)-1)/2) b. x^2=((sqrt(5)+1...

    Text Solution

    |

  6. The value of sin\ (1/2cot^(-1)(-3/4))+cos(1/2cot^(-1)(-3/4)) is/are eq...

    Text Solution

    |

  7. Find the value of tan^(-1)(1/2tan2A)+tan^(-1)(cotA)+tan^(-1)(cot^3A),f...

    Text Solution

    |

  8. For the equation 2x=tan(2tan^(-1)a)+ 2tan \ (tan^(-1)a+tan^(-1)a^3) , ...

    Text Solution

    |

  9. The value of [tan{pi/4+1/2sin^(-1)(a/b)}]^(-1)

    Text Solution

    |

  10. Which of the following pairs of function/functions has same graph? y=...

    Text Solution

    |

  11. The solution set of equation sin^(-1) sqrt(1-x^2) + cos^(-1) x = cot^(...

    Text Solution

    |

  12. The solution set of the equation sin^(-1)sqrt(1-x^2)+cos^(-1)x=cot^(-...

    Text Solution

    |

  13. if 0 lt x lt 1 then tan^(-1)= sqrt(1-x^2)/(1+x^2) is equal to (i) 1/...

    Text Solution

    |

  14. The number of real solutions of tan^(-1)sqrt(x(x+1))+sin^(-1)sqrt(x^2+...

    Text Solution

    |

  15. If [sin^-1x]+[cos^-1x]=0, where 'x' is a non negative real number and ...

    Text Solution

    |

  16. Value of k for which the point (alpha,sin^(-1)alpha)(alpha>0) lies ins...

    Text Solution

    |

  17. Solution set of the inequality sin^(-1)(sin((2x^2+3)/(x^2+1)))lt=pi-5/...

    Text Solution

    |

  18. Consider two geometric progressions a1,a2,a3,......a0 & b1, b2, b3,......

    Text Solution

    |

  19. The sum of the infinite terms of the series cot^(-1)(1^2+3/4)+cot^(-1)...

    Text Solution

    |

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

    Text Solution

    |