Home
Class 12
MATHS
Prove that tan (sin^(-1)x) = x/(sqrt(1...

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

Text Solution

Verified by Experts

The correct Answer is:
`LHS = RHS`
Promotional Banner

Topper's Solved these Questions

  • INVERSE TRIGONOMETRIC FUNCTIONS

    PREMIERS PUBLISHERS|Exercise SOLVED TO EXERCISE 4.1|12 Videos

  • INVERSE TRIGONOMETRIC FUNCTIONS

    PREMIERS PUBLISHERS|Exercise SOLVED TO EXERCISE 4.2|13 Videos

  • DISCRETE MATHEMATICS

    PREMIERS PUBLISHERS|Exercise Problems For Practice|30 Videos

  • MODEL QUESTION PAPER - II

    PREMIERS PUBLISHERS|Exercise PART-IV|8 Videos

Similar Questions

Explore conceptually related problems

Prove that cot (cos^(-1) x) = x/(sqrt(1-x^(2))) |x| lt 1

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

Prove that sin^(-1). ((x + sqrt(1 - x^(2))/(sqrt2)) = sin^(-1) x + (pi)/(4) , where - (1)/(sqrt2) lt x lt(1)/(sqrt2)

Prove that tan^(-1).(1)/(sqrt(x^(2) -1)) = (pi)/(2) - sec^(-1) x, x gt 1

Find (dy)/(dx)," if "y= sin^(-1)x +sin^(-1)sqrt(1-x^(2)), 0 lt x lt 1 .

Prove that 0 lt int_0^1(x^7dx)/((1+x^8)^(1/3)) lt 1/8

Find (dy)/(dx) in the following : y= cos^(-1) ((2x)/(1+x^(2))), -1 lt x lt1 .

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

Find (dy)/(dx) in the following : y= sin^(1)((1-x^(2))/(1+x^(2))), 0 lt x lt 1 .

PREMIERS PUBLISHERS-INVERSE TRIGONOMETRIC FUNCTIONS -PROBLEMS FOR PRACTICE ( ANSWER THE FOLLOWING QUESTIONS ):
  1. Prove that tan (sin^(-1)x) = x/(sqrt(1-x^(2))) - 1 lt x lt 1 .

    Text Solution

    |

  2. Find the principal value of sin^(-1)"" (1)/(sqrt(2))

    Text Solution

    |

  3. Find the principal value of sin^(-1) (sin (-pi/6))

    Text Solution

    |

  4. Find the principal value of sin^(1) (sin ((6pi)/7))

    Text Solution

    |

  5. Find the principal values of cos^(-1)""(1)/(2)

    Text Solution

    |

  6. Find the principal value of cos^(-1) cos ((-pi)/4)

    Text Solution

    |

  7. Find the principal value of cos^(-1)cos ((7pi)/6)

    Text Solution

    |

  8. Find the principal value of tan^(-1)((-1)/(sqrt(3)))

    Text Solution

    |

  9. Find the principal value of tan^(-1)tan ((3pi)/4)

    Text Solution

    |

  10. Find the principal value of tan^(-1) (-1)

    Text Solution

    |

  11. Find the domain sin^(-1) (3 - 4x^(2))

    Text Solution

    |

  12. Find the value of sin^(-1) (sin . (5pi)/8 cos . (pi)/8 - cos . (5pi...

    Text Solution

    |

  13. Find the value of cos^(-1)(cos . (5pi)/9 cos .pi/9 - sin . (5pi)/9 ...

    Text Solution

    |

  14. Find the domain of cos^(-1) ((3+sinx)/4)

    Text Solution

    |

  15. Find the value of 2 cos^(-1). (sqrt(3))/2 + sin^(-1). (sqrt(3))/2

    Text Solution

    |

  16. Evaluate : cos^(-1) cos ((6pi)/5) +cos^(-1) cos ((4pi)/3)

    Text Solution

    |

  17. Simplify : tan^(-1)(1) - cos^(-1) ((-1)/2) +sin^(-1) ((-sqrt(3))/2)

    Text Solution

    |

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

    Text Solution

    |

  19. Find the range of tan^(-1)((2x)/(1+x^2))

    Text Solution

    |

  20. Find the derivatives of the following : cos^(-1)((1-x^(2))/(1+x^(2))...

    Text Solution

    |

  21. Prove the following : cos^(-1)((1-x^(2))/(1+x^(2)))=sin^(-1) ((2x)/(...

    Text Solution

    |