Home
Class 12
MATHS
Show that :2tan^(-1)x+sin^(-1)(2x)/(1+x^...

Show that :`2tan^(-1)x+sin^(-1)(2x)/(1+x^2)` is constant for `xgeq1,` find that constant.

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • INDEFINITE INTEGRALS

    RD SHARMA ENGLISH|Exercise All Questions|1443 Videos

  • LINEAR PROGRAMING

    RD SHARMA ENGLISH|Exercise All Questions|4 Videos

Similar Questions

Explore conceptually related problems

If 2tan^(-1)x+sin^(-1)((2x)/(1+x^2) ) is independent of x then :

sin (tan ^(-1)2x)

Solve tan^(-1) x + sin^(-1) x = tan^(-1) 2x

If |x| le 1 , then 2tan^(-1)x + sin^(-1)((2x)/(1+x^(2))) is equal to

Show that '(1-cos 2x + sin x)/(sin 2x + cos x) = tan x'

Evaluate: int(sin(tan^(-1)x)/(1+x^2)dx )

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

If sin^(-1)(2x)/(1+x^2)=tan^(-1)(2x)/(1-x^2) , then find the value of xdot

Prove 2sin^(-1)x=tan^(-1)((2xsqrt(1-x^2))/(1-2x^2))

If y = 2tan^(-1)x+sin^(-1)((2x)/(1+x^(2))) , then "………"lt y lt "………" .

RD SHARMA ENGLISH-INVERSE TRIGONOMETRIC FUNCTION-All Questions
  1. Prove that: tan^(-1){(cos2alphasec2beta+cos2betasec2alpha)/2}=tan^(-1...

    Text Solution

    |

  2. Prove that: (alpha^3)/2cos e c^2(1/2tan^(-1)alpha/beta)+(beta^3)/2sec^...

    Text Solution

    |

  3. Show that :2tan^(-1)x+sin^(-1)(2x)/(1+x^2) is constant for xgeq1, find...

    Text Solution

    |

  4. Prove that: tan^(-1)((1-x^2)/(2x))+cot^(-1)((1-x^2)/(2x))=pi/2

    Text Solution

    |

  5. Simplify each of the following: cos^(-1)(3/5cosx+4/5sinx) , where -(...

    Text Solution

    |

  6. Write the following functions in the simplest form: tan^(-1){x/(sqrt...

    Text Solution

    |

  7. Evaluate each of the following: cot^(-1)(1/(sqrt(3)))-cos e c^(-1)(-2)...

    Text Solution

    |

  8. For the principal values, evaluate the following: cot^(-1)(-1)+cos e ...

    Text Solution

    |

  9. Prove that: (i)tan^(-1){(sqrt(1+cosx)+sqrt(1-cosx))/(sqrt(1+cosx)-sqr...

    Text Solution

    |

  10. Evaluate each of the following: sin^(-1)(sinpi/3) (ii) cos^(-1)(cos(2...

    Text Solution

    |

  11. If cos e c^(-1)x+cos e c^(-1)y+cos e c^(-1)z=-(3pi)/2, find the value ...

    Text Solution

    |

  12. For the principal values, evaluate the following: tan^(-1)sqrt(3)-se...

    Text Solution

    |

  13. Find the principal values of cot^(-1)sqrt(3) and cot^(-1)(-1)

    Text Solution

    |

  14. For the principal values, evaluate the following: sin^(-1)(-(sqrt(3))...

    Text Solution

    |

  15. The value of tan{cos^(-1)1/(5sqrt(2))-sin^(-1)4/(sqrt(17))} is (sqrt(2...

    Text Solution

    |

  16. sin(cot^(-1)(tan(cos^(-1)x))) is equal to a) x b) sqrt(1-x^2) c) 1/x d...

    Text Solution

    |

  17. Write the value of tan^(-1){2sin(2cos^(-1)(sqrt(3))/2)}dot

    Text Solution

    |

  18. Write the principal value of cos^(-1)(cos680^0)dot

    Text Solution

    |

  19. What is the principal value of sin^(-1)(-(sqrt(2))/2)?

    Text Solution

    |

  20. Write the principal value of cos^(-1)(cos((2pi)/3))+sin^(-1)(sin((2pi)...

    Text Solution

    |