Home
Class 12
MATHS
Prove that |tan^(-1)x-tan^(-1)y|lt=|x-y|...

Prove that `|tan^(-1)x-tan^(-1)y|lt=|x-y|AAx , y in Rdot`

Promotional Banner

Topper's Solved these Questions

  • 3D COORDINATION SYSTEM

    CENGAGE PUBLICATION|Exercise DPP 3.1|11 Videos

  • APPLICATION OF INTEGRALS

    CENGAGE PUBLICATION|Exercise All Questions|143 Videos

Similar Questions

Explore conceptually related problems

Prove that tan^(-1)(1/(x+y))+tan^(-1)(y/(x^2+xy+1) )= cot^(-1)x .

y = a tan^(-1) x + b

Prove that , tan^(-1)""x+ tan^(-1) ""y+tan^(-1)""z= tan ^(-1)""(x+y+z-xyz)/(1-xy-yz-zx)

Prove that tan^(-1) x + tan^(-1).(1)/(x) = {(pi//2,"if" x gt 0),(-pi//2," if " x lt 0):}

Draw the graph of y=tan^(-1)x+cot^(-1)x

Prove that tan ^(-1)""(1)/(x+y)+ tan ^(-1)""(y)/(x^(2)+xy+1)= cot ^(-1)x.

prove that . Tan ^(-1) x- tan ^(-1 )y = cos ^(-1) (1+xy)/(sqrt((1+x^(2))(1+y^(2)))).

Solve the following equations : tan^(-1)(x/y)-"tan"^(-1)(x-y)/(x+y) is equal to

Prove that tan^(-1)x+"tan"^(-1)(2x)/(1-x^(2))=tan^(-1)((3x-x^(3))/(1-3x^(2))),|x|lt1/(sqrt(3))

Prove that tan^(-1){x/(a+sqrt(a^2-x^2))}=1/2sin^(-1)(x/a) ,-a lt x lt a

CENGAGE PUBLICATION-APPLICATION OF DERIVATIVES-All Questions
  1. Prove that if 2a0^2lt15a all roots of x^5-a0x^4+3ax^3+bx^2+cx+d=0 can...

    Text Solution

    |

  2. If f(x) is continuous in [a , b] and differentiable in (a,b), then pro...

    Text Solution

    |

  3. Prove that |tan^(-1)x-tan^(-1)y|lt=|x-y|AAx , y in Rdot

    Text Solution

    |

  4. Using Lagranges mean value theorem, prove that (b-a)/bltlog(b/a)lt(b-a...

    Text Solution

    |

  5. If a > b >0, with the aid of Lagranges mean value theorem, prov...

    Text Solution

    |

  6. Let f(x)a n dg(x) be two functions which are defined and differentiabl...

    Text Solution

    |

  7. If the tangent to the curve x y+a x+b y=0 at (1,1) is inclined at an a...

    Text Solution

    |

  8. Find the condition that the line A x+B y=1 may be normal to the curve ...

    Text Solution

    |

  9. Prove that the curve (x/a)^n+(y/b)^n=2 touches the straught line x/a+y...

    Text Solution

    |

  10. If the equation of the tangent to the curve y^2=a x^3+b at point (2,3)...

    Text Solution

    |

  11. The ength of substangent to the curve y=e^(x//a) is :

    Text Solution

    |

  12. In the curve x^a y^b=K^(a+b) , prove that the potion of the tangent in...

    Text Solution

    |

  13. Does there exists line/lines which is/are tangent to the curve y=sinx ...

    Text Solution

    |

  14. If the tangent at (1,1) on y^2=x(2-x)^2 meets the curve again at P , t...

    Text Solution

    |

  15. The length of normal to the curve x=a(theta+sintheta),y=a(1-costheta) ...

    Text Solution

    |

  16. Determine p such that the length of the sub-tangent and sub-normal is ...

    Text Solution

    |

  17. If f(x)a n dg(x) are continuous functions in [a , b] and are different...

    Text Solution

    |

  18. Let f(x)a n dg(x) be two functions which are defined and differentiabl...

    Text Solution

    |

  19. On the curve x^3=12y the abscissa changes at a faster rate than the or...

    Text Solution

    |

  20. The length x of a rectangle is decreasing at the rate of 5cm/s and the...

    Text Solution

    |