Results 1 to 3 of 3

Math Help - Proving Trig Identities help

  1. #1
    Newbie
    Joined
    Aug 2007
    Posts
    11

    Proving Trig Identities help

    I'm stumped on these two problems for my homework, if someone could help me out I'd appreciate it.

    1.) (tan2x+1)(cos2x-1)=-tan2x


    2.) 2+cos2x-3cos4x=sin2x(2+3cos2x)



    note the #'s in front of the x are supposed to be exponents
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Newbie
    Joined
    Nov 2008
    Posts
    2

    Smile (:

    It took me a little while to think of the first one, but since I'm studying for a test, I decided to just try it until it worked, and I finally got it.

    1) (tan^2x+1)(cos^2x-1) = -tan^2x

    Using the Left Hand Side

    (tan^2x+1)(cos^2x-1)
    = **(sec^2x)(cost^2x-1)
    = (1/cos^2x)(cos^2x-(cos^2x+sin^2x)
    = (1/cos^2x)(cos^2x-cos^2x-sin^2x)
    = (1/cos^2x)(-sin^2x)
    = *(-sin^2x/cos^2x)
    = -tan^2x

    * where: tan^2x =sin^2x/cos^2x
    ** sec^2= 1 + tan^2x
    derived from:
    1 = sin^2x + cos^2x (divided by cos^2x)

    2) 2+cos^2x-3cos^4x = sin^2x(2+3cos^2x)

    Using the Right hand side

    sin^2x(2+3cos^2x)
    = 2sin^2x + 3sin^2cos^2x
    = 2(1-cos^2x)+3(1-cos^2x)cos^2x
    = 2-2cos^2x+3(cos^2-cos^4)
    = 2-2cos^2x+3cos^2-3cos^4)
    = 2+cos^2x-3cos^4x

    Using the Identities:
    1 = sin^2x + cos^2x
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,802
    Thanks
    691
    Hello, WolfMV!

    1)\;\;(\tan^2\!x+1)(\cos^2\!x-1)\:=\:-\tan^2\!x

    We have: . \underbrace{(\tan^2\!x+1)}_{\sec^2\!x}\,\bigg[-\underbrace{(1-\cos^2\!x)}_{\sin^2\!x}\bigg] \;=\;\sec^2\!x(-\sin^2\!x)

    . . . = \;\frac{1}{\cos^2\!x}(-\sin^2\!x) \;=\;-\frac{\sin^2\!x}{\cos^2\!x} \;=\;-\left(\frac{\sin x}{\cos x}\right)^2 \;=\;-\tan^2\!x



    2)\;\; 2+\cos^2\!x-3\cos^4\!x\;=\;\sin^2\!x(2+3\cos^2\!x)

    \text{Factor: }\;2 + \cos^2\!x -3\cos^4\!x \;=\;\underbrace{(1-\cos^2\!x)}_{\sin^2\!x}(2 + 3\cos^2\!x) \;=\;\sin^2\!x(2 + 3\cos^2\!x)

    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. [SOLVED] Proving Trig identities help!
    Posted in the Trigonometry Forum
    Replies: 2
    Last Post: March 28th 2011, 04:33 AM
  2. Proving Trig Identities
    Posted in the Trigonometry Forum
    Replies: 3
    Last Post: April 23rd 2009, 04:13 PM
  3. Proving Trig Identities
    Posted in the Pre-Calculus Forum
    Replies: 4
    Last Post: February 25th 2009, 09:56 AM
  4. Proving Trig Identities?
    Posted in the Trigonometry Forum
    Replies: 3
    Last Post: January 7th 2009, 08:24 AM
  5. HELP! Trig-Proving Identities
    Posted in the Trigonometry Forum
    Replies: 1
    Last Post: April 22nd 2006, 08:48 AM

Search Tags


/mathhelpforum @mathhelpforum