Results 1 to 4 of 4
Like Tree2Thanks
  • 2 Post By Soroban

Math Help - How is this derived?

  1. #1
    Member maxpancho's Avatar
    Joined
    Jun 2014
    From
    Mathville
    Posts
    247
    Thanks
    28

    Question How is this derived?

    $\sin^2(2x)=\dfrac{1-\cos(4x)}{2}=\dfrac{1}{2}(1-\cos(4x))$


    I know these two identities should be used here, but I'm not sure what's exactly legal when they are used together at the same time.

    $\sin^2(x)+\cos^2(x)=1$
    $\sin(2x)=2\sin(x)\cos(x)$
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Member maxpancho's Avatar
    Joined
    Jun 2014
    From
    Mathville
    Posts
    247
    Thanks
    28

    Re: How is this derived?

    That is, I don't understand how did we arrive at the second step.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,905
    Thanks
    765

    Re: How is this derived?

    Hello, maxpancho!

    \text{How is this derived? }\:\sin^2(2x)\;=\;\dfrac{1-\cos(4x)}{2}

    We have: .$\cos(A+B) \:=\:\cos A\cos B - \sin A\sin B$

    Let A=B\!:\;\cos(2A) \:=\:\cos^2\!A - \sin^2\!A \;=\;(1-\sin^2\!A) - \sin^2\!A

    . . . . . . . . . \cos(2A) \:=\:1-2\sin^2\!A \quad\Rightarrow\quad 2\sin^2\!A \;=\;1 - \cos(2A)

    . . . . . . . . . . \sin^2\!A \;=\;\frac{1-\cos(2A)}{2}

    Let A =2x\!:\;\;\sin^2(2x) \;=\;\frac{1-\cos(4x)}{2}

    Thanks from maxpancho and sakonpure6
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Member maxpancho's Avatar
    Joined
    Jun 2014
    From
    Mathville
    Posts
    247
    Thanks
    28

    Re: How is this derived?

    Hello, Soroban, and thank you very much.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Derived Functions
    Posted in the Algebra Forum
    Replies: 1
    Last Post: September 15th 2013, 09:08 PM
  2. derived sets
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: July 1st 2011, 03:54 AM
  3. Derived Set Proof
    Posted in the Differential Geometry Forum
    Replies: 2
    Last Post: October 16th 2009, 09:22 PM
  4. What is the derived set of and closure of [3,7)
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: October 11th 2009, 07:02 AM
  5. derived subgroup
    Posted in the Advanced Algebra Forum
    Replies: 9
    Last Post: May 25th 2009, 12:16 PM

Search Tags


/mathhelpforum @mathhelpforum