Results 1 to 6 of 6

Thread: Proving Trig Formulas

  1. #1
    Newbie
    Joined
    May 2010
    Posts
    2

    Proving Trig Formulas

    Hey, I have a few questions I just can't seem to get down, looking for some help here...
    1) sin2x = 2csc2x-tanx
    1-cos2x

    2) cos(x+y)cos(x-y)=(cosx)^2 +(cosy)^2 -1

    3) (cosx)^6 + (sinx)^6 = 1-3(sinx)^2 + 3(sinx)^4

    Thanks in advance!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor harish21's Avatar
    Joined
    Feb 2010
    From
    Dirty South
    Posts
    1,036
    Thanks
    10
    Quote Originally Posted by orca432 View Post
    Hey, I have a few questions I just can't seem to get down, looking for some help here...
    1) sin2x = 2csc2x-tanx
    1-cos2x

    2) cos(x+y)cos(x-y)=(cosx)^2 +(cosy)^2 -1

    3) (cosx)^6 + (sinx)^6 = 1-3(sinx)^2 + 3(sinx)^4

    Thanks in advance!
    You need to show you work too..

    (2) $\displaystyle cos(x+y)cos(x-y) = (cosx.cosy-sinx.siny)(cosx.cosy+sinx.siny)$

    $\displaystyle = (cos^2x.cos^2y) - (sin^2x.sin^2y)$

    $\displaystyle = (cos^2x.cos^2y) - [(1-cos^2x)(1-cos^2y)]$

    multiply and cancel to complete the proof
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor harish21's Avatar
    Joined
    Feb 2010
    From
    Dirty South
    Posts
    1,036
    Thanks
    10
    for (3)

    $\displaystyle (cosx)^6+(sinx)^6$

    $\displaystyle = (cos^{2}x)^3 + (sin^{2}x)^3$

    since $\displaystyle (a^3+b^3) = (a+b)(a^2-ab+b^2)$, you can write:

    $\displaystyle = (cos^{2}x+sin^{2}x)(cos^{4}x-cos^{2}x. sin^{2}x+sin^{4}x)$

    $\displaystyle = 1 (cos^{4}x-cos^{2}x. sin^{2}x+sin^{4}x)$

    convert all cosines into sines and your proof will be complete.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Newbie
    Joined
    May 2010
    Posts
    2
    Quote Originally Posted by harish21 View Post
    for (3)

    $\displaystyle (cosx)^6+(sinx)^6$

    $\displaystyle = (cos^{2}x)^3 + (sin^{2}x)^3$

    since $\displaystyle (a^3+b^3) = (a+b)(a^2-ab+b^2)$, you can write:

    $\displaystyle = (cos^{2}x+sin^{2}x)(cos^{4}x-cos^{2}x. sin^{2}x+sin^{4}x)$

    $\displaystyle = 1 (cos^{4}x-cos^{2}x. sin^{2}x+sin^{4}x)$

    convert all cosines into sines and your proof will be complete.
    When I converted them, I got $\displaystyle 1-(sinx)^2+(sinx)^4$, anyone care to help me?
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor harish21's Avatar
    Joined
    Feb 2010
    From
    Dirty South
    Posts
    1,036
    Thanks
    10
    Quote Originally Posted by orca432 View Post
    When I converted them, I got $\displaystyle 1-(sinx)^2+(sinx)^4$, anyone care to help me?
    $\displaystyle cos^{4}x = (cos^{2}x)^2= (1-sin^{2}x)^2=1-2sin^{2}x+sin^{4}x$

    substitute this in what you had earlier on

    $\displaystyle 1 . (cos^{4}x-cos^{2}x. sin^{2}x+sin^{4}x)$

    $\displaystyle =1-2sin^{2}x+sin^{4}x-[(1-sin^{2}x). sin^{2}x]+sin^{4}x$

    finish it...
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Master Of Puppets
    pickslides's Avatar
    Joined
    Sep 2008
    From
    Melbourne
    Posts
    5,237
    Thanks
    33
    Here's a little more.

    $\displaystyle \cos^{4}x-\cos^{2}x \sin^{2}x+\sin^{4}x$

    $\displaystyle \cos^{2}x\cos^{2}x-\cos^{2}x \sin^{2}x+\sin^{4}x$

    $\displaystyle (1-\sin^2{x})(1-\sin^2{x})-(1-\sin^2{x}) \sin^{2}x+\sin^{4}x$

    Now expand this.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. [SOLVED] Help with trig addition and subtraction formulas.
    Posted in the Trigonometry Forum
    Replies: 10
    Last Post: Dec 4th 2011, 02:10 PM
  2. Deriving an equation using Trig formulas
    Posted in the Trigonometry Forum
    Replies: 1
    Last Post: Mar 23rd 2011, 03:39 PM
  3. Proving a Helix using Frenet Formulas
    Posted in the Calculus Forum
    Replies: 0
    Last Post: Oct 11th 2010, 08:43 AM
  4. [SOLVED] Need help with Trig Sum Formulas Question
    Posted in the Trigonometry Forum
    Replies: 6
    Last Post: Mar 27th 2010, 04:10 PM
  5. Proving Multiple Angel Formulas
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: Nov 10th 2009, 02:42 PM

Search Tags


/mathhelpforum @mathhelpforum