Results 1 to 2 of 2

Math Help - I need help solving a trig proof

  1. #1
    Newbie
    Joined
    Nov 2008
    Posts
    1

    Red face I need help solving a trig proof

    I have been trying to solve this proof for hours and I just can't figure it out: (1+sinx+cosx)/(1+sinx-cosX)=(1+cosx)/sinx
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member flyingsquirrel's Avatar
    Joined
    Apr 2008
    Posts
    802
    Hi,

    I'd do it this way :

    <br />
\begin{aligned}\frac{1+\sin x+\cos x}{1+\sin x -\cos x}&=<br />
\frac{(1+\sin x+\cos x)(1+\sin x +\cos x)}{(1+\sin x -\cos x)(1+\sin x +\cos x)}\\&=\frac{(1+\sin x+\cos x)^2}{(1+\sin x -\cos x)(1+\sin x +\cos x)}\end{aligned}

    Note that the denominator of the RHS looks like (a-b)(a+b)=a^2-b^2 with a = 1+\sin x and b=\cos x hence

    <br />
\begin{aligned}<br />
\frac{1+\sin x+\cos x}{1+\sin x -\cos x}&=\frac{(1+\sin x)^2+2\cos x(1+\sin x)+\cos^2x}{(1+\sin x)^2-\cos^2x}\\<br />
&=\frac{1+2\sin x+\sin^2x+2\cos x(1+\sin x)+\cos^2x}{1+2\sin x+\sin^2x-\cos^2x}\\<br />
\end{aligned}

    Using 1-\cos^2x=\sin^2x to simplify the denominator and \cos^2x=1-\sin^2x to simplify the numerator,

    <br />
\begin{aligned}<br />
\frac{1+\sin x+\cos x}{1+\sin x -\cos x}&=\frac{1+2\sin x+\sin^2x+2\cos x(1+\sin x)+1-\sin^2x}{\sin^2x+2\sin x+\sin^2x}\\<br />
&=\frac{2+2\sin x+2\cos x(1+\sin x)}{2\sin x(1+\sin x)}\\<br />
&=\frac{2(1+\sin x)+2\cos x(1+\sin x)}{2\sin x(1+\sin x)}\\&=\frac{2(1+\sin x)(1+\cos x)}{2\sin x(1+\sin x)}\\<br />
&=\frac{1+\cos x}{\sin x}<br />
\end{aligned}
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Trig word problem - solving a trig equation.
    Posted in the Trigonometry Forum
    Replies: 6
    Last Post: March 14th 2011, 07:07 AM
  2. Solving Trig Ids
    Posted in the Trigonometry Forum
    Replies: 2
    Last Post: January 24th 2010, 08:06 AM
  3. Solving trig
    Posted in the Trigonometry Forum
    Replies: 3
    Last Post: January 7th 2010, 02:45 AM
  4. trig solving for x
    Posted in the Trigonometry Forum
    Replies: 1
    Last Post: July 28th 2009, 04:52 AM
  5. Trig help solving.
    Posted in the Trigonometry Forum
    Replies: 1
    Last Post: October 2nd 2006, 08:13 AM

Search Tags


/mathhelpforum @mathhelpforum