Home
Class 12
MATHS
cos^(-1)x+cos^(-1)y+cos^(-1)z=pi ,then p...

`cos^(-1)x+cos^(-1)y+cos^(-1)z=pi` ,then prove that, `x^2+y^2+z^2+xyz=1`

Promotional Banner

Topper's Solved these Questions

  • INTEGRAL CALCULUS

    SHARAM PUBLICATION|Exercise EXAMPLE|188 Videos

  • LINEAR PROGRAMMING

    SHARAM PUBLICATION|Exercise EXAMPLE|37 Videos

Similar Questions

Explore conceptually related problems

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

If "sin"^(-1)x + "sin"^(-1)y +"sin"^(-1)z = pi "prove 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/a) ="cos"^-1(y/b) = theta, "prove that" x^2/a^2 -(2xy)/(ab) "cos" theta +y^2/b^2 ="sin"^2 theta.

If "cos"^(-1)(x/y) +"cos"^-1(y/3)= theta, "prove that" 9x^2- 12xy "cos" theta +4y^2 =36 "sin"^2 theta .

If sin^(-1) x +sin^(-1) y + sin^(-1) z =pi , "show that" x sqrt(1-x^2)+y sqrt(1-y^2) +zsqrt(1-z^2)=2 xyz

If tan^(-1)x +tan^(-1) y +tan^(-1) z=pi/2 . Show that xy+yz+zx =1.

SHARAM PUBLICATION-INVERSE TRIGNOMETRIC FUNCTIONS-EXAMPLE
  1. Solve for x tan^(-1)(x+2)+tan^(-1)(x-2)=tan^(-1)(8/79),x>0.

    Text Solution

    |

  2. Prove that: tan^(-1)(3/4)+tan^(-1)(3/5)-tan^(-1)(8/19)=pi/4

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  5. If "tan"^(-1) x +"tan" ^(-1) y +"tan"^(-1)z -pi show that x+y+z=xyz.

    Text Solution

    |

  6. Prove statement tan ( 2 "tan"^(-1)1/5-pi/4) + 7/17 =0

    Text Solution

    |

  7. Prove that : "tan"^(-1)sqrt((xr)/(yz)) +"tan"^(-1) sqrt((yr)/(yx)) +"...

    Text Solution

    |

  8. If u=cot^(-1)sqrtcos alpha-tan^(-1)sqrt(cosalpha)then prove that sincu...

    Text Solution

    |

  9. Prove the "sin"^(-1) sqrt((x-q)/(p-q))="cos"^(-1)sqrt((p-x)/(p-q))="co...

    Text Solution

    |

  10. Prove the sin^2(sin^(-1) x+sin^(-1) y+sin^(-1)z) =cos^2 (cos^(-1)x +c...

    Text Solution

    |

  11. Prove statement "tan"^(-1) x +"cot"^(-1)(x+1)="tan"^(-1)(x^2+x+1)

    Text Solution

    |

  12. Show that:4(cot^(-1)(3/2)+cosec^(-1)sqrt(26))=pi.

    Text Solution

    |

  13. Show that: tan^(-1)(a-b)/(1+ab)+tan^(-1)(b-c)/(1+bc)+tan^(-1)(c-a)/(1+...

    Text Solution

    |

  14. Show that: tan^(-1)(a-b)/(1+ab)+tan^(-1)(b-c)/(1+bc)+tan^(-1)(c-a)/(1+...

    Text Solution

    |

  15. In a triangle ABC "if" m/A =90^@, "prove that "tan"^(-1) b/(a+b) +"ta...

    Text Solution

    |

  16. If "sin"^(-1)x + "sin"^(-1)y +"sin"^(-1)z = pi "prove that" x^4+y^4+z^...

    Text Solution

    |

  17. If sin^(-1)((x)/(a)) +sin^(-1)((y)/(b)) = sin^(-1)((c^(2))/(ab)), t...

    Text Solution

    |

  18. If "cos"^(-1)(x/y) +"cos"^-1(y/3)= theta, "prove that" 9x^2- 12xy "co...

    Text Solution

    |

  19. In a DeltaABC, if mangleA=90^(@), prove that "tan"^(-1)b/(a+c)+"tan"^(...

    Text Solution

    |

  20. Solve the following equations "tan"^(-1)1/(3)+"tan"^(-1)1/(5)+"tan"^...

    Text Solution

    |