Home
Class 12
MATHS
Differentiate the following functions wi...

Differentiate the following functions with respect to `x` : `tan^(-1){sqrt((1+sinx)/(1-sinx))},-pi/2ltxltpi/ 2`

Text Solution

Verified by Experts

y=`tan^(-1){sqrt((1+sinx)/(1-sinx))}`
=`tan^(-1){sqrt((1+2sin(x/2)cos(x/2))/(1-2sin(x/2)cos(x/2)))}`
=`tan^(-1){sqrt((cos^2(x/2)+sin^2(x/2)+2sin(x/2)cos(x/2))/(cos^2(x/2)+sin^2(x/2)-2sin(x/2)cos(x/2)))}`
=`tan^(-1)((cos(x/2)+sin(x/2))/(cos(x/2)-sin(x/2)))`
=`tan^(-1)((1+tan(x/2))/(1-tan(x/2)))`
=`tan^(-1)tan(pi/4+x/2)`
`dy/dx=1/2`
Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIALS, ERRORS AND APPROXIMATIONS

    RD SHARMA|Exercise Solved Examples And Exercises|102 Videos

  • DIRECTION COSINES AND DIRECTION RATIOS

    RD SHARMA|Exercise Solved Examples And Exercises|67 Videos

Similar Questions

Explore conceptually related problems

Differentiate the following functions with respect to x:tan^(-1){sqrt((1+sin x)/(1-sin x))},-(pi)/(2)

Differentiate the following functions with respect to x:tan^(-1){sqrt((1+cos x)/(1-cos x))}

Differentiate the following functions with respect to x:tan^(-1){sqrt((1+cos x)/(1-cos x))},0

Differentiate the following functions with respect tox tan^(-1)(e^(x))

Differentiate the following functions with respect to x:tan^(-1){sqrt((1+cos x)/(1-cos x))}0

Differentiate the following function with respect of x:x^(n)tan x

Differentiate the following functions with respect to x:tan^(-1)((a+x)/(1-ax))

Differentiate the following functions with respect to x:tan^(-1)((a+x)/(1-ax))

Differentiate the following function with respect of x:(x)/(1+tan x)

Differentiate the following function with respect of x:(x)/(1+tan x)

RD SHARMA-DIFFERENTIATION-Solved Examples And Exercises
  1. Differentiate the following functions with respect to x : tan^(-1){s...

    Text Solution

    |

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

    Text Solution

    |

  3. Differentiate the following functions with respect to x : tan^(-1){s...

    Text Solution

    |

  4. Differentiate the following functions with respect to x : tan^(-1)(s...

    Text Solution

    |

  5. Differentiate the following functions with respect to x : tan^(-1)((a...

    Text Solution

    |

  6. Differentiate the following functions with respect to x : tan^(-1)((...

    Text Solution

    |

  7. Differentiate the following functions with respect to x : tan^(-1)((3...

    Text Solution

    |

  8. y=tan^(-1)((acosx-bsinx)/(bcosx+asinx)), where -pi/2ltxltpiand a/btanx...

    Text Solution

    |

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

    Text Solution

    |

  10. Differentiate the following functions with respect to x : tan^(-1){s...

    Text Solution

    |

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

    Text Solution

    |

  12. Differentiate the following functions with respect to x : tan^(-1){(1+...

    Text Solution

    |

  13. Differentiate the following functions with respect to x : tan^(-1){sqr...

    Text Solution

    |

  14. Differentiate the following functions with respect to x : tan^(-1)(s...

    Text Solution

    |

  15. Differentiate (2^xcotx)/(sqrt(x)) with respect to x .

    Text Solution

    |

  16. Differentiate e^xlogsqrt(x)tanx with respect to x .

    Text Solution

    |

  17. Differentiate (e^x+sinx)/(1+logx) with respect to x .

    Text Solution

    |

  18. Differentiate (sinx-xcosx)/(xsinx+cosx) with respect to xdot

    Text Solution

    |

  19. If y=(1+x)(1+x^2)(1+x^4)(1+x^8)dot(1+x^2^n) , find (dy)/(dx) .

    Text Solution

    |

  20. If f(x)=|cosx| , find f^(prime)(pi/4) and f^(prime)((3pi)/4) .

    Text Solution

    |