Home
Class 12
MATHS
Prove that : tan^(-1)(1/2)+tan^(-1)(1/5)...

Prove that : `tan^(-1)(1/2)+tan^(-1)(1/5)+tan^(-1)(1/8)=pi/4dot`

Text Solution

Verified by Experts

Here, we will use,
`tan^-1x+tan^-1y = tan^-1((x+y)/(1-xy))`
`L.H.S. = tan^-1(1/2)+tan^-1(1/5)+tan^-1(1/8)`
`=tan^-1((1/2+2/5)/(1-1/2(2/5)))+tan^-1(1/8)`
`=tan^-1(7/9)+tan^-1(1/8)`
`=tan^-1((7/9+1/8)/(1-7/9(1/8)))`
`=tan^-1((65/72)/(65/72))`
...
Promotional Banner

Topper's Solved these Questions

  • CUET MOCK TEST 2022

    XII BOARDS PREVIOUS YEAR|Exercise Question|49 Videos

Similar Questions

Explore conceptually related problems

Prove that tan^(-1) (1/8) +tan^(-1) (1/5) =tan^(-1) (1/3)

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

Prove that tan^ (-1)( 1/3) +tan^(-1)( 1/5) + tan^(-1) (1/7 )+tan^(-1) (1/8) = pi/4

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

Prove that tan ^(-1)(1/5) + tan^(-1)(1/7) +tan^(-1)(1/3)+ tan ^(-1)(1/8) = pi/4

Prove that : tan^(-1)(1)/(5)+tan^(-1)(1)/(7)+tan^(-1)(1)/(3)+tan^(-1)(1)/(8)=(pi)/(4)

prove that tan^(-1)(1)+tan^(-1)(2)+tan^(-1)(3)=pi

Prove that : tan^(-1)1/5+tan^(-1)1/7+tan^(-1)1/3+tan^(-1)1/8=pi/4

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

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

XII BOARDS PREVIOUS YEAR-BOARD PAPER SOLUTIONS-All Questions
  1. Evaluate: int(dx)/(x(x^5+3))

    Text Solution

    |

  2. Find the value of k so that the function f defined by f(x)={(kcosx)/(...

    Text Solution

    |

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

    Text Solution

    |

  4. Find the vector and cartesian equations of the line passing through...

    Text Solution

    |

  5. Evaluate: |(cos15^0,sin15^0),(sin75^0,cos75^0)|

    Text Solution

    |

  6. What is the principal value of cos^(-1)cos((2pi)/3)+sin^(-1)sin((2p...

    Text Solution

    |

  7. Let A = {1, 2, 3}, B = {4, 5, 6, 7}and let f = {(1, 4), (2, 5), (3, 6)...

    Text Solution

    |

  8. Evaluate: int0^4(|x|+|x-2|+|x-4|)\ dx

    Text Solution

    |

  9. Evaluate: int(dx)/(sqrt(1-x^2))

    Text Solution

    |

  10. Evaluate: int(a x+b)^3dx

    Text Solution

    |

  11. If a matrix has 5 elements, write all possible orders it can have.

    Text Solution

    |

  12. If A=[[2, 3],[ 5,-2]], write A^(-1) in terms of A

    Text Solution

    |

  13. Using properties of determinants, prove the following: |[1,x,x^2],[...

    Text Solution

    |

  14. Write the projection of the vector hat i- hat j on the vector ha...

    Text Solution

    |

  15. Write the direction-cosines of the line joining the points (1, 0, 0...

    Text Solution

    |

  16. Differentiate the following function with respect to x : (log\ x)^...

    Text Solution

    |

  17. If y=log[x+sqrt(x^2+a^2)\ ] , show that ((x^2+a^2)(d^2\ y)/(dx^2)+x(dy...

    Text Solution

    |

  18. Evaluate: int0^(pi/4)(cos^2x)/(cos^2x+4sin^2x)dx\

    Text Solution

    |

  19. Evaluate: int1^3(x^2+x)dx

    Text Solution

    |

  20. Show that of all the rectangles inscribed in a given fixed circle, ...

    Text Solution

    |