Results 1 to 2 of 2

Thread: Calculate !

  1. #1
    Junior Member
    Joined
    Dec 2009
    Posts
    46

    Calculate !

    Hii !

    $\displaystyle \tan(a)$ and $\displaystyle \tan(b)$ are the solutions of the equation :

    $\displaystyle x^2+\pi x+\sqrt{2}=0$

    calculate: $\displaystyle sin^2(a+b)+\pi\sin(a+b)\cos(a+b)+\sqrt{2}cos^2(a+b )$
    Last edited by Perelman; Feb 3rd 2010 at 09:21 AM.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Opalg's Avatar
    Joined
    Aug 2007
    From
    Leeds, UK
    Posts
    4,041
    Thanks
    10
    Quote Originally Posted by Perelman View Post
    Hii !

    $\displaystyle \tan(a)$ and $\displaystyle \tan(b)$ are the solutions of the equation :

    $\displaystyle x^2+\pi x+\sqrt{2}=0$

    calculate: $\displaystyle \sin^2(a+b)+\pi\sin(a+b)\cos(a+b)+\sqrt{2}\cos^2(a +b)$
    If $\displaystyle \tan a$ and $\displaystyle \tan b$ are the solutions of the equation $\displaystyle x^2+px+q=0$ then $\displaystyle \tan a + \tan b = -p$ and $\displaystyle \tan a\tan b = q$. Thus $\displaystyle \tan(a+b) = \frac{\tan a + \tan b}{1-\tan a\tan b} = \frac{-p}{1-q}$. Also, $\displaystyle \sec^2(a+b) = 1+\tan^2(a+b) = \frac{p^2+(1-q)^2}{(1-q)^2}$, and so $\displaystyle \cos^2(a+b) = \bigl(\sec^2(a+b)\bigr)^{-1} = \frac{(1-q)^2}{p^2+(1-q)^2}$.

    Then $\displaystyle \sin^2(a+b)+p\sin(a+b)\cos(a+b)+q\cos^2(a+b) = \cos^2(a+b)\bigl(\tan^2(a+b)+p\tan(a+b)+q\bigr)$, and you can check by using the results of the previous paragraph that this simplifies to $\displaystyle q$ (which in this case is $\displaystyle \sqrt2$).
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Is it possible to calculate x and y....
    Posted in the Algebra Forum
    Replies: 2
    Last Post: Nov 29th 2010, 01:16 PM
  2. calculate
    Posted in the Algebra Forum
    Replies: 5
    Last Post: Apr 27th 2010, 09:35 AM
  3. Calculate
    Posted in the Calculus Forum
    Replies: 1
    Last Post: Apr 14th 2010, 02:11 AM
  4. Calculate M4
    Posted in the Calculus Forum
    Replies: 5
    Last Post: Mar 29th 2010, 08:44 PM
  5. Calculate this sum
    Posted in the Number Theory Forum
    Replies: 1
    Last Post: Aug 28th 2009, 11:50 PM

Search Tags


/mathhelpforum @mathhelpforum