Home
Class 12
MATHS
Write the following functions in the sim...

Write the following functions in the simplest form :
`tan^(-1) (x/sqrt(a^2-x^2)), |x| lt a`

Text Solution

Verified by Experts

Put x = a `sin theta, theta = sin^(-1)(x/a)`
Then `tan^(-1)(x/sqrt(a^2-x^2)) = tan^(-1)((a sin theta)/sqrt(a^2-a^2 sin^2 theta ))`
`= tan^(-1)((a sin theta)/sqrt(a^2 cos^2 theta)) = tan^(-1) (tan theta) = theta = sin^(-1)(x/a)`
Promotional Banner

Topper's Solved these Questions

  • INVERSE TRIGONOMETRIC FUNCTIONS

    A N EXCEL PUBLICATION|Exercise QUESTION BANK|22 Videos

  • INTEGRALS

    A N EXCEL PUBLICATION|Exercise QUESTION BANK|291 Videos

  • LINEAR PROGRAMMING

    A N EXCEL PUBLICATION|Exercise QUESTION BANK|40 Videos

Similar Questions

Explore conceptually related problems

Write the following functions in the simplest form : tan^(-1)(1/sqrt(x^2 -1)), |x| gt 1

Write the following functions in the simplest form : tan^(-1)((sqrt(1+x^2)-1)/x), x ne 0

Write the following functions in the simplest form : tan^(-1)((3a^2x - x^3)/(a^3- 3ax^2)), a gt 0, -a/sqrt3 le x le a/sqrt3

Write the following functions in the simplest form : tan^(-1) sqrt((1-cos x)/(1+cos x)), 0 lt x lt pi

Write the following functions in the simplest form : tan^(-1)((cos x -sin x)/(cos x + sin x)), -pi/4 lt x lt (3pi)/4

Integrate the following functions x tan^-1x

lntegrate the following function with respect to x, (sin (2 tan ^(-1) x))/(1+x^2)

lntegrate the following function with respect to x : sqrt(2 x-x^2)

lntegrate the following function with respect to x , 1/((1+x^2) tan ^(-1) x)

lntegrate the following function with respect to x: 1/sqrt(2 x-x^2)

A N EXCEL PUBLICATION-INVERSE TRIGONOMETRIC FUNCTIONS-QUESTION BANK
  1. prove that 3 cos^(-1) x = cos^(-1) (4x^3 - 3x), x in [1/2,1]

    Text Solution

    |

  2. Prove that tan^(-1)(2/11) + tan^(-1)(7/24) = tan^(-1)(1/2)

    Text Solution

    |

  3. Prove that 2 tan^(-1)(1/2) + tan^(-1)(1/7) = tan^(-1)(31/17)

    Text Solution

    |

  4. Write the following functions in the simplest form : tan^(-1)((sqrt(...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  7. Write the following functions in the simplest form : tan^(-1)((cos x...

    Text Solution

    |

  8. Write the following functions in the simplest form : tan^(-1) (x/sqr...

    Text Solution

    |

  9. Write the following functions in the simplest form : tan^(-1)((3a^2x...

    Text Solution

    |

  10. Find the value of tan^(-1)[2 cos(2sin^(-1)frac(1)(2) )]

    Text Solution

    |

  11. Find the value of cot(tan^(-1) a + cot^(-1) a)

    Text Solution

    |

  12. Find the values of the following tan frac(1)(2) [sin^(-1)((2x)/(1+x...

    Text Solution

    |

  13. If sin(sin^-1(frac(1)(5))+cos^-1(x))=1

    Text Solution

    |

  14. If tan^(-1) ((x-1)/(x-2)) + tan^(-1) ((x+1)/(x+2)) = pi/4. then find t...

    Text Solution

    |

  15. Find the value of sin^(-1)sin((2pi)/3)

    Text Solution

    |

  16. Find the values of the following : tan^(-1)(tan frac (3pi)4)

    Text Solution

    |

  17. Evaluate tan(sin^-1frac(3)(5)+cot^-1frac(3)(2))

    Text Solution

    |

  18. find the value of cos^-1cos((7pi)/3)

    Text Solution

    |

  19. Find sin(pi/3-sin^(-1)(-1/2)) =

    Text Solution

    |

  20. Find tan^(-1) sqrt3 -sec^(-1)(-2)

    Text Solution

    |