Results 1 to 4 of 4

Math Help - Trig identities.

  1. #1
    Junior Member
    Joined
    May 2010
    Posts
    36

    Trig identities.

    Hi,
    Im having a lot of trouble solving the following trig identities:

    a) secē x-2 sec x cos x + cosē = tanē x - sinē x
    b) tan x + 1/ tanx = 1/sin x cos x




    My working:
    For a):


    Trigonometric identity: secx cosx=1
    Therefore:
    secēx-2 sec x cos x + cosē
    =secēx + cosē-2
    Identity: secēx = 1/cosēx
    Use the Identity:
    secēx + cosē- 2
    1/cos^2x +cosēx-2


    Now I am very confused, really unsure on how to prove this identity. I would greatly appreciate any helpful tips.


    For b)


    tanx+1/tanx =1/(sinx cosx )
    L.H.S:
    Tanx+1/tanx
    Identity: 1/tanx = cotx :
    =tanx+cotx

    Now im completely lost, the R.H.S side is turning out to be "csc x sec x" .

    I would greatly appreciate any helpful tips, since I'm very confused here.


    Thanks
    Last edited by mr fantastic; June 5th 2010 at 05:44 PM. Reason: Edited post title.
    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 spoc21 View Post
    Hi,
    Im having a lot of trouble solving the following trig identities:

    a) secē x-2 sec x cos x + cosē = tanē x - sinē x
    b) tan x + 1/ tanx = 1/sin x cos x




    My working:
    For a):


    Trigonometric identity: secx cosx=1
    Therefore:
    secēx-2 sec x cos x + cosē
    =secēx + cosē-2
    Identity: secēx = 1/cosēx
    Use the Identity:
    secēx + cosē- 2
    1/cos^2x +cosēx-2


    Now I am very confused, really unsure on how to prove this identity. I would greatly appreciate any helpful tips.


    For b)


    tanx+1/tanx =1/(sinx cosx )
    L.H.S:
    Tanx+1/tanx
    Identity: 1/tanx = cotx :
    =tanx+cotx

    Now im completely lost, the R.H.S side is turning out to be "csc x sec x" .

    I would greatly appreciate any helpful tips, since I'm very confused here.


    Thanks
    (b) tanx+\frac{1}{tanx} = \frac{sinx}{cosx} +\frac{1}{\frac{sinx}{cosx}} = \frac{sinx}{cosx}+\frac{cosx}{sinx}

    = \frac{sin^2x+cos^2x}{sinx.cosx} = \frac{1}{sinx.cosx}
    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
    (a) sec^2x-2secx.cosx+cos^2x

    use the identity sec^2x-tan^2x=1 and cos^2x=1-sin^2x

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

    = 1+tan^2x-2+1-sin^2x

    =tan^2x-sin^2x
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Junior Member
    Joined
    May 2010
    Posts
    36
    Quote Originally Posted by harish21 View Post
    (a) sec^2x-2secx.cosx+<b>cos^2x</b>

    use the identity sec^2x-tan^2x=1 and cos^2x=1-sin^2x

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

    = 1+tan^2x-2+1-sin^2x

    =tan^2x-sin^2x
    Thanks harish,
    the cos^2 x in bold is actually only cos^2..would this make a difference? or would the same method you described work?
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. [SOLVED] trig identities
    Posted in the Trigonometry Forum
    Replies: 0
    Last Post: October 12th 2011, 06:31 PM
  2. Trig. Identities
    Posted in the Trigonometry Forum
    Replies: 4
    Last Post: February 9th 2011, 08:19 PM
  3. Trig identities
    Posted in the Trigonometry Forum
    Replies: 4
    Last Post: June 5th 2010, 04:46 PM
  4. Trig identities
    Posted in the Trigonometry Forum
    Replies: 1
    Last Post: December 16th 2008, 08:02 PM
  5. Trig Identities Help!
    Posted in the Math Topics Forum
    Replies: 1
    Last Post: November 30th 2008, 02:04 AM

Search Tags


/mathhelpforum @mathhelpforum