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 , prove that x^2+y^2+z^2+2x y z=1.

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

If cos^(-1)x+cos^(-1)y+cos^(-1)=pi,p rov et h a tx^2+y^2+z^2+2x y z=1.

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 = pi , prove that x^(2) + y^(2) + z^(2) + 2xyz = 1

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

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

If cos^(-1)x+cos^(-1)y+cos^(-1)z=pi,t h e n x^2+y^2+z^2+2x y z=1 2(sin^(-1)x+sin^(-1)y+sin^(-1)z)=cos^(-1)x+cos^(-1)y+cos^(-1)z x y+y z+z x=x+y+z-1 (x+1/x)+(y+1/y)+(z+1/z)geq6

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

Multiply: x^2+4y^2+z^2+2x y+x z-2y z\ by x-2y-z

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) - 4xy cos alpha ...

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

    Text Solution

    |

  6. For the equation 2x=tan(2tan^(-1)a)+2 t a n(tan^(-1)a+tan^(-1)a^3) , w...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  10. If 0ltxlt1, then "tan"^(-1)(sqrt(1-x^(2)))/(1+x) is equal to

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  14. Sum of infinite terms of the series cos^(-1) ( 1^(2) + 3/4) + cot^(-...

    Text Solution

    |

  15. If the numerical value of tan(cos^(-1)((4)/(5))+tan^(-1)((2)/(3)))" i...

    Text Solution

    |

  16. The value of cos[1/2cos^(-1)(cos(-(14pi)/5))]\ is/are a.cos(-(7pi)/...

    Text Solution

    |

  17. Prove that tan^(-1).(1)/(4) + tan^(-1).(2)/(9) = (1)/(2) cos ^(-1).(3)...

    Text Solution

    |

  18. Solve: sin^(-1)(3x)/5+sin^(-1)(4x)/5=sin^(-1)x

    Text Solution

    |

  19. Evaluate: sin(cot^(-1)x) (ii) cos(tan^(-1)x)

    Text Solution

    |

  20. sin(cot^(-1)(tan(tan^(-1)x))),"x" in (0," 1]

    Text Solution

    |