Results 1 to 5 of 5

Math Help - Prove that sin2x-tanx=tanXcos2X

  1. #1
    Newbie
    Joined
    Nov 2009
    Posts
    21

    Prove that sin2x-tanx=tanXcos2X

    Please help me out with this question


    Prove that sin2x-tanx=tanXcos2X


    This is what i did:
    Sin2x-tanx=0
    2sinXcosX-tanx=0
    2sinXcosX-(sinX/cosX)=0


    Donít know how to take it any further to solve it?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    A riddle wrapped in an enigma
    masters's Avatar
    Joined
    Jan 2008
    From
    Big Stone Gap, Virginia
    Posts
    2,551
    Thanks
    11
    Awards
    1
    Quote Originally Posted by mike789 View Post
    Please help me out with this question


    Prove that sin2x-tanx=tanXcos2X


    This is what i did:
    Sin2x-tanx=0
    2sinXcosX-tanx=0
    2sinXcosX-(sinX/cosX)=0


    Don’t know how to take it any further to solve it?

    Hi mik789,

    Here's what I did. I used the left side only.

    \sin 2x - \tan x =

    2\sin x \cos x - \tan x =

    2 \sin x \cos x - \dfrac{\sin x}{\cos x}=

    \dfrac{2 \sin x \cos^2 x-\sin x}{\cos x}=

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

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

    \boxed{\tan x \cos 2x}


    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Nov 2009
    Posts
    21
    Quote Originally Posted by masters View Post

    Hi mik789,

    Here's what I did. I used the left side only.

    \sin 2x - \tan x =

    2\sin x \cos x - \tan x =

    2 \sin x \cos x - \dfrac{\sin x}{\cos x}=

    \dfrac{2 \sin x \cos^2 x-\sin x}{\cos x}=

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

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

    \boxed{\tan x \cos 2x}


    But how do you turn 2(cos^2)x-1 into cos2x
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Newbie
    Joined
    Nov 2009
    Posts
    21
    thanks. you cancelled the cos^2 to get cos2x
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Junior Member
    Joined
    Nov 2010
    Posts
    50
    Quote Originally Posted by mike789 View Post
    thanks. you cancelled the cos^2 to get cos2x
    not exactly.the double angle formula for cos states that cos2x = 2cos^2x - 1 . You cannot "cancel" away cos on it's own. It is always accompanied by a something(in this case,x)

    and also for proving, you are only allowed to algebraically manipulate one side such that it looks like the other. cross multiplication and things like that are not allowed because if you do that it means that it is an equation and not an identity(correct me if I am wrong here)
    Last edited by arccos; November 15th 2010 at 05:26 PM.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Prove:(tanx/(1+tanx)) = (sinx/(sinx+cosx))
    Posted in the Trigonometry Forum
    Replies: 7
    Last Post: February 2nd 2011, 08:46 PM
  2. [SOLVED] Value of sin2x and cos2x when tanx=5/3
    Posted in the Trigonometry Forum
    Replies: 11
    Last Post: July 3rd 2009, 06:07 AM
  3. prove tanx =
    Posted in the Calculus Forum
    Replies: 2
    Last Post: June 24th 2009, 02:10 AM
  4. prove that sin2x+sin2y=2sin(x+y)cos(x-y)
    Posted in the Trigonometry Forum
    Replies: 2
    Last Post: March 29th 2009, 02:15 PM
  5. Prove that secx=[2(cosxsin2x-sinxcos2x)]/sin2x
    Posted in the Trigonometry Forum
    Replies: 3
    Last Post: March 28th 2009, 09:11 AM

Search Tags


/mathhelpforum @mathhelpforum