Results 1 to 3 of 3

Math Help - proof

  1. #1
    Newbie
    Joined
    Mar 2008
    Posts
    14

    proof

    Can someone help me on this -

    Prove that tan(sin^-1x) = x/sqrt(1-x^2) for |x| < 1 and x not equal to 0

    Thanks !
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Global Moderator

    Joined
    Nov 2005
    From
    New York City
    Posts
    10,616
    Thanks
    9
    Quote Originally Posted by darkangel View Post
    Can someone help me on this -

    Prove that tan(sin^-1x) = x/sqrt(1-x^2) for |x| < 1 and x not equal to 0

    Thanks !
    \tan(\sin^{-1} x) = \frac{\sin (\sin^{-1} x)}{\cos (\sin^{-1} x)} = \frac{x}{\cos (\sin^{-1} x)}.

    \cos^2 (\sin^{-1} x) = 1 - \sin^2(\sin^{-1} x) = 1-x^2\implies \cos x (\sin^{-1} x) = \sqrt{1-x^2} (since the value is positive).

    Thus, we get \frac{x}{\sqrt{1-x^2}}.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Mar 2008
    Posts
    14
    Thanks ThePerfectHacker !!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 5
    Last Post: October 19th 2010, 10:50 AM
  2. Replies: 0
    Last Post: June 29th 2010, 08:48 AM
  3. [SOLVED] direct proof and proof by contradiction
    Posted in the Number Theory Forum
    Replies: 2
    Last Post: February 27th 2010, 10:07 PM
  4. Proof with algebra, and proof by induction (problems)
    Posted in the Discrete Math Forum
    Replies: 8
    Last Post: June 8th 2008, 01:20 PM
  5. proof that the proof that .999_ = 1 is not a proof (version)
    Posted in the Advanced Applied Math Forum
    Replies: 4
    Last Post: April 14th 2008, 04:07 PM

Search Tags


/mathhelpforum @mathhelpforum