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

Write the following functions in the simplest form: (i)`tan^(-1){x/(sqrt(a^2-x^2))},\ -a< x < a` (ii)`tan^(-1){sqrt((a-x)/(a+x))},\ -a< x < a`

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

Write the following functions in the simplest form: tan^(-1){x/(sqrt(a^2-x^2))}

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

Write the following functions in the simplest form: (i) sin^(-1){x/(sqrt(x^2+a^2))} (ii) cos^(-1){x/(sqrt(x^2+a^2))}

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

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

Write the following function in the simplest form: tan^(-1)((3a^2x-x^3)/(a^3-3a x^2)), a >0;(-a)/(sqrt(3))lt=xlt=a/(sqrt(3))

Write the following function in the simplest form: tan^(-1)((3a^2x-x^3)/(a^3-3a x^2)), a >0;(-a)/(sqrt(3))lt=xlt=a/(sqrt(3))

Write the following function in the simplest form: tan^(-1)((3a^2x-x^3)/(a^3-3a x^2)), a >0;(-a)/(sqrt(3))lt=xlt=a/(sqrt(3))

Write each of the following in the simplest form: tan^(-1){x/(a+sqrt(a^2-x^2))} where -a < x < a (ii) sin^(-1){(x+sqrt(1-x^2))/(sqrt(2))} , -1/2 < x < 1/(sqrt(2))

Write the following function in the simplest form: tan^-1 sqrt((1-cosx)/(1+cosx))

RD SHARMA ENGLISH-INVERSE TRIGONOMETRIC FUNCTION-All Questions
  1. Prove that: tan^(-1){(sqrt(1+cosx)+sqrt(1-cosx))/(sqrt(1+cosx)-sqrt(1-...

    Text Solution

    |

  2. Prove that: cot^(-1){(sqrt(1+sinx)+sqrt(1-sinx))/(sqrt(1+sinx)-sqrt(1-...

    Text Solution

    |

  3. Write the following functions in the simplest form: (i)tan^(-1){x/(s...

    Text Solution

    |

  4. Write the following functions in the simplest form: (i)sin^(-1){x/(s...

    Text Solution

    |

  5. Prove that: tan^(-1){(sqrt(1+x)-sqrt(1-x))/(sqrt(1+x)+sqrt(1-x))}=pi/4...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  8. Simplify: sin^(-1)(5/(13)cosx+(12)/(13)sinx)

    Text Solution

    |

  9. Simplify: sin^(-1)((sinx+cosx)/(sqrt(2))) where - π/4 < x < π/4

    Text Solution

    |

  10. Simplify: cos^(-1)((sinx+cosx)/(sqrt(2))),π/4 < x <(5π)/4

    Text Solution

    |

  11. Simplify each of the following: sin^(-1)((sinx+cosx)/(sqrt(2))),\ pi...

    Text Solution

    |

  12. Evaluate the following: sin^(-1)(sin10) (ii) sin^(-1)(sin5)

    Text Solution

    |

  13. Evaluate the following: cos^(-1)(cos10) (ii) tan^(-1){tan(-6)}

    Text Solution

    |

  14. Evaluate each of the following: sin^(-1)(sin(pi/6)) (ii) sin^(-1)(si...

    Text Solution

    |

  15. Evaluate each of the following: (i)sin^(-1)(sin((13pi)/7)) (ii) sin^...

    Text Solution

    |

  16. Evaluate each of the following: sin^(-1)(sin3) (ii) sin^(-1)(sin4)

    Text Solution

    |

  17. Evaluate each of the following: sin^(-1)(sin12) (ii) sin^(-1)(sin2)

    Text Solution

    |

  18. Evaluate each of the following: (i)cos^(-1){cos(-pi/4)} (ii) cos^(-1...

    Text Solution

    |

  19. Evaluate each of the following: (i)cos^(-1)(cos((13pi)/6)) (ii) cos^...

    Text Solution

    |

  20. Evaluate each of the following: cos^(-1)(cos5) (ii) cos^(-1)(cos12)

    Text Solution

    |