Home
Class 11
MATHS
If x+y+z=x y z prove that (2x)/(1-x^2)+(...

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

Text Solution

Verified by Experts

`x+y+z = xyz`
Let `x = tanA, y = tanB, z = tanC`
Then,
`tanA+tanB+tanC = tanAtanBtanC`
It implies that,
`A+B+C = npi,` where `n in I`
`=>2A+2B+2C = 2npi`
`:. tan2A+tan2B+tan2C = tan2Atan2Btan2C`
...
Promotional Banner

Topper's Solved these Questions

  • STRAIGHT LINES

    CENGAGE|Exercise Solved Examples And Exercises|482 Videos

Similar Questions

Explore conceptually related problems

If x+y+z=xzy , prove that : (2x)/(1-x^2) + (2y)/(1-y^2) + (2z)/(1-z^2) = (2x)/(1-x^2) (2y)/(1-y^2) (2z)/(1-z^2)

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

If xy+yz+xz=1, then prove that (x)/(1-x^(2))+(y)/(1-y^(2))+(z)/(1-z^(2))=(4xyz)/((1-x^(2))(1-y^(2))(1-z^(2)))

If x+y+z=xyz, then value of (x)/(1-x^(2))+(y)/(1-y^(2))+(z)/(1-z^(2))(x)/(1-x^(2))(y)/(1-y^(2))(z)/(1-z^(2))

If xy+yz+zx=1 show that (x)/(1-x^(2))+(y)/(1-y^(2))+(z)/(1-z^(2))=(4xyz)/((1-x^(2))(1-y^(2))(1-z^(2)))

If xy + yz + zx = 1 , show that x/(1-x^(2)) +y/(1-y^(2)) + z/(1-z^(2))= (4xyz)/((1-x^(2))(1-y^(2)) (1-z^(2)))

If xy + yz + zx = 1 , show that x/(1-x^(2)) +y/(1-y^(2)) + z/(1-z^(2))= 4xyz/((1-x^(2))(1-y^(2)) (1-z^(2)))

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

CENGAGE-TRIGONOMETRIC FUNCTIONS-Solved Examples And Exercises
  1. Prove that a(bcosC-ccosB)=b^2-c^2

    Text Solution

    |

  2. If 4sin^4x+cos^4x=1,then x is equal to (n in Z) (a)npi (b) npi+-...

    Text Solution

    |

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

    Text Solution

    |

  4. If in a triangle a cos^2C/2+ c cos^2A/2=(3b)/2, then find the relatio...

    Text Solution

    |

  5. Evaluate cosacos2acos3a cos 999 a , where a=(2pi)/(1999)dot

    Text Solution

    |

  6. If sin^3theta+sinthetacos^2theta=1,t h e ntheta is equal to (n in Z)...

    Text Solution

    |

  7. Find the number of pairs of integer (x , y) that satisfy the followin...

    Text Solution

    |

  8. Prove that (4cos^2 9^0-3)(4cos^2 27^0-3)=tan9^0dot

    Text Solution

    |

  9. Let A D be a median of the A B Cdot If A Ea n dA F are medians of ...

    Text Solution

    |

  10. Find the value of cos12^0+cos84^0+cos156^0+cos132^0

    Text Solution

    |

  11. If no solution of 3siny+12sin^3x=a lies on the line y=3x , then a in ...

    Text Solution

    |

  12. Find the angle theta whose cosine is equal to its tangent.

    Text Solution

    |

  13. If sin^2x-2sinx-1=0 has exactly four different solutions in x in [0,np...

    Text Solution

    |

  14. If in triangle the angles are in the ratio as 1:2:3 , prove that the ...

    Text Solution

    |

  15. A balloon is observed simultaneously from three points A, B and C on a...

    Text Solution

    |

  16. A general solution of tan^2theta+cos2theta=1 is (n in Z) npi=pi/4 (...

    Text Solution

    |

  17. In an equilateral triangle, three coins of radii 1 unit each are kept ...

    Text Solution

    |

  18. Prove that tanpi/(10) is a root of polynomial equation 5x^4-10 x^2+1=0...

    Text Solution

    |

  19. If sinx+cosx=sqrt(y+1/y) for x in [0,pi] , then x=pi/4 (b) y=0 y=1 ...

    Text Solution

    |

  20. Which of the following pieces of data does NOT uniquely determine an ...

    Text Solution

    |