Results 1 to 7 of 7

Math Help - trig proof

  1. #1
    Newbie
    Joined
    May 2011
    Posts
    5

    trig proof

    \frac{sin^{4} \alpha}{a}+ \frac{cos ^{4}\alpha }{b}= \frac{1}{a+b}

    Prove that:

    \frac{sin^{8} \alpha}{a^{3}}+ \frac{cos ^{8} \alpha }{b^{3}}= \frac{1}{(a+b)^{3}}

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

  2. #2
    Senior Member abhishekkgp's Avatar
    Joined
    Jan 2011
    From
    India
    Posts
    495
    Thanks
    1
    Quote Originally Posted by andtom View Post
    \frac{sin^{4} \alpha}{a}+ \frac{cos ^{4}\alpha }{b}= \frac{1}{a+b}
    take sin^{2} \alpha=x. then cos^{2} \alpha=1-x.

    Now substitute in the given equation. SOLVE the quadratic. the roots are nice! you will get sin^{2} \alpha=\frac{a}{a+b} . Substitute this below


    Prove that:

    \frac{sin^{8} \alpha}{a^{3}}+ \frac{cos ^{8} \alpha }{b^{3}}= \frac{1}{(a+b)^{3}}

    Thanks in advance
    did this help?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    May 2011
    Posts
    5
    Nope, I still cannot prove it :/
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor FernandoRevilla's Avatar
    Joined
    Nov 2010
    From
    Madrid, Spain
    Posts
    2,162
    Thanks
    45
    Quote Originally Posted by andtom View Post
    Nope, I still cannot prove it

    Show what roots do you obtain for

    \dfrac{x^2}{a}+\dfrac{(1-x)^2}{b}=\dfrac{1}{a+b}
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    May 2011
    Posts
    5
    so there's only 1 root
    since \Delta = 0,
    x=sin^{2}\alpha=\frac{2a}{2(a+b)}=\frac{a}{a+b}
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Senior Member abhishekkgp's Avatar
    Joined
    Jan 2011
    From
    India
    Posts
    495
    Thanks
    1
    Quote Originally Posted by andtom View Post
    so there's only 1 root
    since \Delta = 0,
    x=sin^{2}\alpha=\frac{2a}{2(a+b)}=\frac{a}{a+b}
    correct!
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Newbie
    Joined
    May 2011
    Posts
    5
    OK, i got it
    Thank you guys
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. trig proof help
    Posted in the Trigonometry Forum
    Replies: 9
    Last Post: December 13th 2011, 08:03 AM
  2. Trig proof for sec^2
    Posted in the Trigonometry Forum
    Replies: 2
    Last Post: July 11th 2010, 11:40 PM
  3. trig proof help
    Posted in the Trigonometry Forum
    Replies: 6
    Last Post: November 4th 2009, 01:02 PM
  4. Trig proof - urg
    Posted in the Trigonometry Forum
    Replies: 4
    Last Post: May 13th 2009, 06:57 AM
  5. Trig Proof Help
    Posted in the Trigonometry Forum
    Replies: 1
    Last Post: February 19th 2007, 02:55 PM

Search Tags


/mathhelpforum @mathhelpforum