Home
Class 12
MATHS
If y=cot^(-1){(sqrt(1+sinx)+sqrt(1-sinx)...

If `y=cot^(-1){(sqrt(1+sinx)+sqrt(1-sinx))/(sqrt(1+sinx)-sqrt(1-sinx))}.` Show that `(dy)/(dx)` is independent of `x.`

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIALS, ERRORS AND APPROXIMATIONS

    RD SHARMA ENGLISH|Exercise All Questions|107 Videos

  • DIRECTION COSINES AND DIRECTION RATIOS

    RD SHARMA ENGLISH|Exercise All Questions|90 Videos

Similar Questions

Explore conceptually related problems

If y="tan"^(-1)((sqrt(1+sinx)+sqrt(1-sinx)))/((sqrt(1+sinx)-sqrt(1-sinx)))," find "(dy)/(dx).

int(sinx)/(sqrt(1+sinx))dx

" If "y=cot^(-1)[(sqrt(1+sinx)+sqrt(1-sinx))/(sqrt(1+sinx)-sqrt(1-sinx))](0ltxltpi//2)," then "(dy)/(dx)=

If y=cot^(-1)[(sqrt(1+sinx)+sqrt(1-sinx))/(sqrt(1+sinx)-sqrt(1-sinx))] , (0 lt x lt pi/2) , then (dy)/(dx)=

If y=cot^(-1)[(sqrt(1+sinx)+sqrt(1-sinx))/(sqrt(1+sinx)-sqrt(1-sinx))] , (0 lt x lt pi/2) , then (dy)/(dx)=

cot^(-1)((sqrt(1+sinx)+sqrt(1-sinx))/(sqrt(1+sinx)-sqrt(1-sinx)))=(x)/(2), x in (0,(pi)/(4))

Differentiate tan^(-1){(sqrt(1+sinx)+sqrt(1-sinx))/(sqrt(1+sinx)-sqrt(1-sinx))} , 0 < x < pi

The value of cot^(-1){(sqrt(1-sinx)+sqrt(1+sinx))/(sqrt(1-sinx)-sqrt(1+sinx))} , where (pi)/2ltxltpi , is

Prove that: cot^(-1)((sqrt(1+sinx)+sqrt(1-sinx))/(sqrt(1+sinx)-sqrt(1-sinx)))=x/2, x in (0,pi/4)

The value of cot^(-1){(sqrt(1-sinx)+sqrt(1+sinx))/(sqrt(1-sinx) -sqrt(1+sinx))} is (0 lt x lt (pi)/(2))

RD SHARMA ENGLISH-DIFFERENTIATION-All Questions
  1. If y=sin^(-1)((2x)/(1+x^2))+sec^(-1)((1+x^2)/(1-x^2)),0ltxlt1, prove t...

    Text Solution

    |

  2. Differentiate the following function with respect to x : tan^(-1)(...

    Text Solution

    |

  3. If y=cot^(-1){(sqrt(1+sinx)+sqrt(1-sinx))/(sqrt(1+sinx)-sqrt(1-sinx))}...

    Text Solution

    |

  4. Find (dy)/(dx), when x=(e^t+e^(-t))/2 \ a n d \ y=(e^t-e^(-t))/2

    Text Solution

    |

  5. Find (dy)/(dx), when x=a e^(theta)(sintheta-costheta),y=a e^(theta)(si...

    Text Solution

    |

  6. Find (dy)/(dx), when x=a(theta+sintheta)a n dy=a(1-costheta)

    Text Solution

    |

  7. Differentiate the following function with respect to x : tan^(-1)(...

    Text Solution

    |

  8. Find (dy)/(dx), when x=(3a t)/(1+t^2)" and "y =(3a t^2)/(1+t^2)

    Text Solution

    |

  9. Differentiate the following function with respect to x : tan^(-1)(...

    Text Solution

    |

  10. Find (dy)/(dx), y=e^x+10^x+x^x

    Text Solution

    |

  11. Differentiate the following function with respect to x : tan^(-1){...

    Text Solution

    |

  12. Differentiate the following function with respect to x : sin^(-1)(...

    Text Solution

    |

  13. Differentiate the following function with respect to x:sin(x^x)

    Text Solution

    |

  14. Differentiate the following function with respect to x : (logx)^(logx)

    Text Solution

    |

  15. Differentiate the following function with respect to x: 10^(logsin...

    Text Solution

    |

  16. If y=logsqrt((1+tanx)/(1-tanx)),"Prove that " (dy)/(dx)=sec2x

    Text Solution

    |

  17. If y=log(sqrt(x)+sqrt(1/x)), prove that (dy)/(dx)=(x-1)/(2x(x+1))

    Text Solution

    |

  18. If y=x/(x+2) , prove that x(dy)/(dx)=(1-y)y

    Text Solution

    |

  19. Find (dy)/(dx), y=(sinx)^(cosx)+(cosx)^(sinx)

    Text Solution

    |

  20. If y=(x-1)log(x-1)-(x+1)log(x+1), prove : (dy)/(dx)=log((x-1)/(1+x))

    Text Solution

    |