Home
Class 12
MATHS
If x + y + z = xyz, prove that (3x -x^(3...

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) * (3y- y^(3))/(1-3x)^(2)* (3z- z^(3))/(1-3z)^(2)`.

Promotional Banner

Topper's Solved these Questions

  • Circular Functions, Identities

    A DAS GUPTA|Exercise Exercise|300 Videos

  • Circles

    A DAS GUPTA|Exercise EXERCISE|122 Videos

  • COMPLEX NUMBERS

    A DAS GUPTA|Exercise EXERCISE|224 Videos

Similar Questions

Explore conceptually related problems

(3x-x^(3))/(1-3x^(2))+(3y-y^(3))/(1-3y^(2))+(3z-z^(3))/ (1-3z^(2))=((3x-x^(3))/(1-3x^(2)))((3z-z^(3))/(1-3z^(2) ))(((3y-y^(3))/(1-3y^(2))))

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

Find ((x^(2)-y^(2))^(3) + (y^(2) -z^(2))^(3)+ (z^(2) -x^(2))^(3))/((x-y)^(3) + (y-z)^(3) + (z-x)^(3))

The value of the expression ((x ^(2) - y ^(2)) ^(3) + ( y ^(2) - z ^(2)) ^(3) + (z ^(2) - x ^(2)) ^(3))/((x - y) ^(3) + ( y - z) ^(3) + (z - x ) ^(3)) is

verify that: x^(3)+y^(3)+z^(3)-3xyz=((1)/(2))(x+y+z)((x-y)^(2)+(y-z)^(2)+(z-x)^(2))

Prove that x^(3)+y^(3)+z^(3)-3xyz=(1)/(2)(x+y+z)[(x-y)^(2)+(y-z)^(2)+(z-x)^(2)]

A DAS GUPTA-Circular Functions, Identities -Exercise
  1. If cos(beta - gamma) * cos(gamma - alpha)* cos(alpha - beta) + 1 = 0 ...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  4. If A + B + C = pi then show that cot theta = cot A + cot B + cot C ⇔ s...

    Text Solution

    |

  5. If theta = pi/7 prove that cos theta* cos 2theta * cos 3theta = 1/8

    Text Solution

    |

  6. If alpha = 2pi/7 prove that tan alpha *tan 2alpha + tan 2alpha* tan 4a...

    Text Solution

    |

  7. If alpha = 2pi/7 prove that sec alpha + sec 2alpha + sec 3alpha = -4.

    Text Solution

    |

  8. Prove that sin pi/14* sin 3pi/14 * sin 5pi/14 = 1/8.

    Text Solution

    |

  9. Show that :sin pi/7 *sin 2pi/7* sin3pi/7 = sqrt7/8

    Text Solution

    |

  10. If u = sec theta + tan theta then tan theta in terms of u is.

    Text Solution

    |

  11. If sin x + cos x = m(ne pm 1) and sec x + cosec x = n then n in terms ...

    Text Solution

    |

  12. If alpha gt 0 such that tan(x + alpha) = tan x for all x in R then the...

    Text Solution

    |

  13. If theta = 5pi/9 the sign of the expression cos theta + sin theta is.

    Text Solution

    |

  14. If 5cos 2t + 12sin 2t = lambda sin(2t -tan^(-1)mu) where lambda, mu ar...

    Text Solution

    |

  15. If cos A = 3/4 then the value of 32sin( A/2)* sin (5A/2) is.

    Text Solution

    |

  16. If sin(theta + 3alpha) = 3sin(alpha - theta) then tan theta in terms o...

    Text Solution

    |

  17. If 0 lt beta lt alpha lt gamma and cos(alpha + beta) = 4/5, sin(alpha...

    Text Solution

    |

  18. If 4nalpha = pi then the numerical value tan alpha* tan 2alpha *tan 3...

    Text Solution

    |

  19. Let sin^(3)x* sin 3x = sum(m=0)^(n) cm cos mx be an identity in x wher...

    Text Solution

    |

  20. If (cos (alpha1- alpha2))/(cos (alpha1+ alpha2)) = (cos (alpha3+ alph...

    Text Solution

    |