Results 1 to 3 of 3
Like Tree1Thanks
  • 1 Post By Prove It

Math Help - Need help with this question!!!

  1. #1
    Junior Member
    Joined
    Mar 2013
    From
    Australia
    Posts
    63

    Need help with this question arctan...

    I am having trouble with this question please help
    Show that arctan(x) = arccos(1/(√(1+x2)))= arcsin(x/(√(1+x2))
    Last edited by calmo11; March 11th 2013 at 12:43 AM.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,672
    Thanks
    1490

    Re: Need help with this question!!!

    \displaystyle \begin{align*} y &= \arctan{(x)} \\ \tan{(y)} &= x \\ \frac{\sin{(y)}}{\cos{(y)}} &= x \\ \frac{\sqrt{1 - \cos^2{(y)}}}{\cos{(y)}} &= x \\ \sqrt{1 - \cos^2{(y)}} &= x\cos{(y)} \\ 1 - \cos^2{(y)} &= x^2\cos^2{(y)} \\ 1 &= \left( 1 + x^2  \right) \cos^2{(y)} \\ \frac{1}{1 + x^2} &= \cos^2{(y)} \\ \frac{1}{\sqrt{1 + x^2}} &= \cos{(y)} \\ y &= \arccos{\left( \frac{1}{\sqrt{1 + x^2}} \right)} \end{align*}

    Now follow a similar process for the second part.
    Thanks from calmo11
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Mar 2013
    From
    Australia
    Posts
    63

    Re: Need help with this question!!!

    Thankyou very much, helped me out perfectly
    Follow Math Help Forum on Facebook and Google+

Search Tags


/mathhelpforum @mathhelpforum