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

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

Promotional Banner

Topper's Solved these Questions

  • INVERSE TRIGONOMETRIC FUNCTIONS

    ACCURATE PUBLICATION|Exercise QUESTIONS CARRYING 1 MARK - TYPE-III (TRUE OR FALSE QUESTIONS)|30 Videos

  • INDEFINITE INTEGRALS

    ACCURATE PUBLICATION|Exercise QUESTIONS CARRYING 4 MARKS|15 Videos

  • LINEAR PROGRAMMING

    ACCURATE PUBLICATION|Exercise QUESTIONS CARRYING 6 MARKS |7 Videos

Similar Questions

Explore conceptually related problems

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

Prove that : tan^-1 x +tan^-1 2x/(1-x^2) = tan^-1 ((3x-x^3)/(1-3x^2)), |x| < 1/sqrt3

Prove that tan^(-1)((x)/(1+sqrt(1-x^(2))))=(1)/(2)sin^(-1)x .

Prove that tan^(-1)((sqrt(1-x^(2)))/(1+x))=(1)/(2)cos^(-1)x

Prove that tan2x=(2tanx)/(1-tan^2 x)

Let tan^(-1) y = tan^(-1) x + tan^(-1) ((2x)/(1 -x^(2))), " where " |x| lt (1)/(sqrt3) . Then a value of y is

Differentiate tan^(-1) ((3x - x^3)/(1 - 3x^2)) w.r.t. tan^(-1)((2x)/(1 - x^2))

ACCURATE PUBLICATION-INVERSE TRIGONOMETRIC FUNCTIONS-QUESTIONS CARRYING 4 MARKS
  1. If sin[cot^(-1)(x+1)]=cos(tan^(-1)x), then find x.

    Text Solution

    |

  2. Solve the following equation cos(tan^(-1)x)=sin(cot^(-1)""3/4).

    Text Solution

    |

  3. Solve the following equations : (i) 2tan^(-1)(cos(2x))=tan^(-1)(2cos...

    Text Solution

    |

  4. Prove that : sin^(-1)""8/17+sin^(-1)""3/5=sin^(-1)""77/85=tan^(-1)""77...

    Text Solution

    |

  5. Prove that : sin^(-1)""3/5+sin^(-1)""8/17=cos^(-1)""36/85.

    Text Solution

    |

  6. Write the value of tan^(-1)[2sin(2cos^(-1)""sqrt(3)/2)].

    Text Solution

    |

  7. Write the principle value of tan^(-1)(1)+cos^(-1)(-1/2).

    Text Solution

    |

  8. Find the value of the following : tan^(-1)(1)+cos^(-1)(-1/2)+sin^(-1...

    Text Solution

    |

  9. Find the value of the following : cos^(-1)(1/2)+2sin^(-1)(1/2)

    Text Solution

    |

  10. Find the value of the following : cos^(-1)(1/2)-2sin^(-1)(1/2)

    Text Solution

    |

  11. Write the value of cos^(-1)(-1/2)+2sin^(-1)(1/2)

    Text Solution

    |

  12. Prove the following: cos[tan^-1{sin(cot^-1x)}]=sqrt((1+x^2)/(2+x^2))

    Text Solution

    |

  13. If sin[cot^(-1)(x+1)]=cos(tan^(-1)x), then find x.

    Text Solution

    |

  14. Solve the following equation cos(tan^(-1)x)=sin(cot^(-1)""3/4).

    Text Solution

    |

  15. Solve the following equations : (i) 2tan^(-1)(cos(2x))=tan^(-1)(2cos...

    Text Solution

    |

  16. Prove that : sin^(-1)""8/17+sin^(-1)""3/5=sin^(-1)""77/85=tan^(-1)""77...

    Text Solution

    |

  17. Prove that : sin^(-1)""3/5+sin^(-1)""8/17=cos^(-1)""36/85.

    Text Solution

    |

  18. Prove that cos^(-1)""(12)/(13)+cos^(-1)""(4)/(3)=tan^(-1)""(56)/(33)

    Text Solution

    |

  19. Prove that : 2tan^(-1)(sqrt((a-b)/(a+b))tan""x/2)=cos^(-1)((acosx+b)/(...

    Text Solution

    |

  20. Prove that tan^(-1)x+"tan"^(-1)(2x)/(1-x^(2))=tan^(-1)((3x-x^(3))/(1-3...

    Text Solution

    |