1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Math Problem

  1. Mar 2, 2006 #1
    Can anyone help me solve this equation,

     
  2. jcsd
  3. Mar 2, 2006 #2
    What have you done so far? Solutions are not just given away in this forum.

    Is it really "solve for x" or is it "prove this"?
     
  4. Mar 2, 2006 #3
    prove this.
    I can't seem to get rid of the bottom and make it 1 + tan(x) + cot(x)
     
    Last edited: Mar 2, 2006
  5. Mar 2, 2006 #4
    Hmmm, I haven't tried this problem, but just a tip, instead of writing cot as 1/tanx write it as cos/sin. Makes things simpler.

    The only thing I can suggest is get common denominators on the left side.

    Wait, are you trying to prove the identity?
     
  6. Mar 2, 2006 #5
    Hmm...
    [tex]
    \begin{gathered}
    \frac{{\cot x}}
    {{1 - \tan x}} + \frac{{\tan x}}
    {{1 - \cot x}} = 1 + \tan x + \cot x \Rightarrow \hfill \\
    \frac{1}
    {{\left( {1 - \tan x} \right)\tan x}} + \frac{{\tan ^2 x}}
    {{\tan x - 1}} = \frac{{\tan ^2 x + \tan x + 1}}
    {{\tan x}} \Rightarrow \hfill \\
    \frac{{1 - \tan ^3 x}}
    {{1 - \tan x}} = \frac{{\tan ^2 x + \tan x + 1}}
    {{\tan x}} \Rightarrow \hfill \\
    \left( {1 - \tan ^3 x} \right)\tan x = \left( {1 - \tan x} \right)\left( {\tan ^2 x + \tan x + 1} \right) \Rightarrow \hfill \\
    \tan x - \tan ^4 x = \tan ^2 x + \tan x + 1 - \tan ^3 x - \tan ^2 x - \tan x \Rightarrow \hfill \\
    \tan x\left( {1 - \tan ^3 x} \right) = 1 - \tan ^3 x \Rightarrow \tan x = 1 \Rightarrow {\text{Mistake?}} \hfill \\
    \end{gathered} [/tex]
     
  7. Mar 3, 2006 #6
    Line 3 should be
    [tex]\frac{1-tan^3x}{(1-tanx)tanx}=\frac{1+tanx+tan^2x}{tanx}[/tex]

    -Dan
     
  8. Mar 3, 2006 #7

    0rthodontist

    User Avatar
    Science Advisor

    Well, multiply through by tan x
    (1 - tan^3(x))/((tan x)(1 - tan x))
    Now you can factor the numerator as a difference of cubes, and reduce.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Math Problem
  1. Maths problem (Replies: 2)

  2. Math problems (Replies: 5)

  3. Math problem (Replies: 6)

  4. Math Problem (Replies: 5)

Loading...