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

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

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

Prove that : sin(tan^(-1)1) = 1/sqrt2

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

Prove that tan^(-1)""(2)/(11)+tan^(-1)""(7)/(24)=(1)/(2)cos^(-1)""(3)/(5)

Let a, b and c be positive real numbers. Then prove that tan^(-1) sqrt((a(a + b + c))/(bc)) + tan^(-1) sqrt((b (a + b + c))/(ca)) + tan^(-1) sqrt((c(a + b+ c))/(ab)) = pi

Prove that : "tan"(pi/(4)+1/(2)"cos"^(-1)a/(b))+"tan"(pi/(4)-1/(2)"cos"^(-1)a/(b))=(2b)/(a) .

Prove that tan^-1(x/(sqrt(a^2 - x^2)) = sin^-1 (x/a), |x| < a.

Prove that : tan (A - B) = (tan A-tanB)/(1+tan A tanB) .

If y = 2/(sqrt(a^2 - b^2)) "tan"^(-1) (sqrt((a + b)/(a - b)) " tan " x/2) , prove that (dy)/(dx) = 1/(a - b cos x)

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

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

    |