Home
Class 12
MATHS
Prove that cos (tan^(-1)(sin(cot^-1x)))...

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

Promotional Banner

Topper's Solved these Questions

  • Integrals

    JMD PUBLICATION|Exercise Exercise|70 Videos

  • Liner Programming

    JMD PUBLICATION|Exercise EXAMPLE|22 Videos

Similar Questions

Explore conceptually related problems

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

Prove that : tan^-1 x + cot^-1(x+1) = tan^-1(x^2 + x +1)

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

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

Prove that : tan^-1[(sqrt(1+x^2) - sqrt(1-x^2))/(sqrt1+x^2 + sqrt(1-x^2))] = pi/4 - 1/2cos^-1x^2

Prove that sec [cot^-1{sin(tan^-1 (cosec(cos^-1 a)))}] = sqrt(3-a^2), where |a| < 1

Prove that cot(cosec^-1x) = sqrt(x^2 - 1) for x ge 1

Prove that derivative of tan^(-1)((sqrt(1 + x^2) - 1)/(x)) w.r.t. tan^(-1) x is independent of x.

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

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

JMD PUBLICATION-INVERSE TRIGONOMETRIC FUNCTIONS-EXAMPLE
  1. Domain of the function f (x) = sin^-1 x is equal to :

    Text Solution

    |

  2. Principal value of cos^-1 (-frac{1}{2}) is :

    Text Solution

    |

  3. Find the value of tan(sin^-1 frac{3}{5} + cot^-1 frac{3}{2}).

    Text Solution

    |

  4. Principal value of cos^-1 (-frac{1}{2}) is :

    Text Solution

    |

  5. Find dy/dx when: y= tan^-1((2x)/(1-x^2))

    Text Solution

    |

  6. Prove that tan^(-1)sqrtx = 1/2cos^(-1) ((1-x)/(1+x)), x in [0,1]

    Text Solution

    |

  7. Prove that sqrt((1+sinA)/(1-sinA))=(1+sinA)/cosA .

    Text Solution

    |

  8. Show that : tan^-1 frac{1}{3} + tan^-1 frac{1}{5}=frac{1}{2} cos^-1 fr...

    Text Solution

    |

  9. Prove that : tan^(-1) (1) + tan ^-1 (2) + tan^(-1) (3) = pi1

    Text Solution

    |

  10. Solve the 2 tan^-1 (cos x) = tan^-1 (2 cosec x).

    Text Solution

    |

  11. Show that: tan^-1 (frac {1-x}{1+x})= frac {1}{2} tan^-1(frac{1-x^2}{2x...

    Text Solution

    |

  12. Prove that : 2 tan^-1 frac{1}{5} + tan^-1 frac{1}{8}= tan^-1 frac{4}{7...

    Text Solution

    |

  13. Prove that : tan^-1[(sqrt(1+x) - sqrt(1-x))/(sqrt1+x + sqrt1-x)] = pi/...

    Text Solution

    |

  14. Find the value 2 tan^(-1)(1/5) + sec^(-1) ((5sqrt2)/7)+ 2tan^(-1)(1/8)

    Text Solution

    |

  15. Prove that : sin^-1 (frac{3}{5}) + cos^-1 (frac{5}{sqrt26}) = tan^-1 (...

    Text Solution

    |

  16. Solve for x: tan^-1 (x+1) + tan^-1(x-1) = tan^-1 frac{8}{31}, x > 0

    Text Solution

    |

  17. Prove that : cos^-1 frac{12}{13} + sin^-1 frac{4}{5}= tan^-1 frac{63}{...

    Text Solution

    |

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

    Text Solution

    |

  19. tan^-1 frac{63}{16}= sin^-1 frac{5}{13}+cos^-1 frac{3}{5}

    Text Solution

    |

  20. If tan^-1 ((x-1)/(x-2))+tan^-1((x+1)/(x+2))=pi/4, then find the value ...

    Text Solution

    |