Home
Class 12
MATHS
If x+y+z=xyz, prove that x/(1-x^2)+ y/(1...

If `x+y+z=xyz`, prove that `x/(1-x^2)+ y/(1-y^2)+z/(1-z^2)`
`=(4xyz)/((1-x^2)(1-y^2)(1-z^2))`

Promotional Banner

Topper's Solved these Questions

  • THREE DIMENSIONAL GEOMETRY

    MBD PUBLICATION|Exercise QUESTION BANK|523 Videos

  • VECTORS

    MBD PUBLICATION|Exercise QUESTION BANK|138 Videos

Similar Questions

Explore conceptually related problems

If x+y+z=xyz , prove that (3x-x^3)/(1-3x^2)+(3y-y^3)/(1-3y^2)+(3z-z^3)/(1-3z^2) = (3x-x^3)/(1-3x^2) cdot(3y-y^3)/(1-3y^2)cdot(3z-z^3)/(1-3z^2)

Prove that |{:(x^2+1,xy,xz),(xy,y^2+1,yz),(xz,yz,z^2+1):}|=1+x^2+y^2+z^2

Prove that |[x, y, z],[x^2, y^2, z^2], [x^3, y^3, z^3]|=xyz(x-y)(y-z)(z-x)

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

using the properties of determinants prove that |{:(1,x+y,x^2+y^2),(1,y+z,y^2+z^2),(1,z+x,z^2+x^2):}|=(x-y)(y-z)(z-x)

Prove that x^3+y^3+z^3-3xyz =(x+y+z)(x+omegay+omega^2z)(x+yomega^2+z omega)

Show that |{:(1,x, x ^(3)),(1,y,y ^(3)),(1,z,z^(3)):}| = (x-y) (y-z) (z-x) (x + y + z)

MBD PUBLICATION-TRIGONOMETRIC FUNCTIONS-QUESTION BANK
  1. Show that 2^ncostheta cdot cos2thetacdotcos2^2theta......cos2^(n-1)t...

    Text Solution

    |

  2. Prove that tan2^ntheta/(tantheta) =(1+sec2theta)(1+sec2^2theta)....(1+...

    Text Solution

    |

  3. If x+y+z=xyz, prove that x/(1-x^2)+ y/(1-y^2)+z/(1-z^2) =(4xyz)/((1-x...

    Text Solution

    |

  4. If x+y+z=xyz, prove that (3x-x^3)/(1-3x^2)+(3y-y^3)/(1-3y^2)+(3z-z^3)/...

    Text Solution

    |

  5. Ifsin^4alpha/a+cos^4alpha/b=1/(a+b) show that sin^8alpha/a^3+cos^8alph...

    Text Solution

    |

  6. The number of solutions of 2sintheta-1=0 is.

    Text Solution

    |

  7. If cosalpha=cosbeta, then alpha+beta=

    Text Solution

    |

  8. The number of solution(s) of 2sectheta+1=0 is.

    Text Solution

    |

  9. If tantheta=tanalpha and 90ltalphalt180, then ' theta ' can be in th...

    Text Solution

    |

  10. If tanx cdot tan 2x cdot tan 7x =tanx+tan2x+tan7x, then x=

    Text Solution

    |

  11. For value of theta, sintheta+costheta=sqrt2

    Text Solution

    |

  12. The number of values of x for which cos^2x=1 and x^2le 4 is

    Text Solution

    |

  13. In the 1st quardrant the solution of tan^2theta=3 is

    Text Solution

    |

  14. The least positive value of theta for which 1 + tan theta=0 and sqrt2 ...

    Text Solution

    |

  15. The least positive value of x for which tan 3x=tan x is

    Text Solution

    |

  16. Find the principal solution of the following equations:sintheta=sin2th...

    Text Solution

    |

  17. Find the principal solution of the following equations:sqrt3 sintheta-...

    Text Solution

    |

  18. Find the principal solution of the following equations:cos^2theta+sint...

    Text Solution

    |

  19. Find the principal solution of the following equations:sin 4x+sin 2x=0

    Text Solution

    |

  20. Find the principal solution of the following equations:sinx+cosx=frac{...

    Text Solution

    |