Results 1 to 2 of 2
Like Tree1Thanks
  • 1 Post By Soroban

Thread: Verify trigonometric identity

  1. #1
    Junior Member
    Joined
    Mar 2013
    From
    Unreals
    Posts
    52

    Verify trigonometric identity

    Hi!

    Is my solution for the problem correct?
    If so, what's the 'right' way to write it up?

    $\displaystyle \displaystyle \cos x(\cot x + \tan x) = \csc x$



    $\displaystyle \displaystyle \cos x\left(\frac{\text{cos}x}{\text{sin}x}\, +\, \frac{\text{sin}x}{\text{cos}x}\right)$

    $\displaystyle \frac{\text{cos}^2x}{\text{sin}x}\,+\,\frac{\text{ cos}x\text{sin}x}{\text{cos}x}$

    $\displaystyle \frac{1-\text{sin}^2x}{\text{sin}x}\,+\,\text{sin}x$

    $\displaystyle \frac{{1-\text{sin}^2x\,+\,\text{sin}^2x}}{{\text{sin}x}}$

    $\displaystyle \frac1{\text{sin}x} \equiv \csc$
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    12,028
    Thanks
    849

    Re: Verify trigonometric identity

    Hello, Unreal

    Your work is correct . . . It was a bit hard to follow.


    $\displaystyle \text{Prove: }\:\cos x(\cot x + \tan x) \:=\: \csc x$
    $\displaystyle \text{Left side: }\:\cos x\left(\frac{\cos x}{\sin x} + \frac{\sin x}{\cos x}\right) \;\;=\;\;\cos x\cdot\frac{\overbrace{\cos^2\!x+\sin^2\!x}^{\text {This is 1}}}{\sin x\cos x}$

    . . . . . . . . . . $\displaystyle =\;\;\cos x\cdot\frac{1}{\sin x\cos x} \;\;=\;\;\frac{1}{\sin x} \;\;=\;\; \csc x $
    Thanks from Unreal
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. [SOLVED] Verify that this is an identity.
    Posted in the Pre-Calculus Forum
    Replies: 3
    Last Post: Jul 27th 2011, 09:14 AM
  2. Replies: 6
    Last Post: Mar 21st 2010, 08:17 PM
  3. verify an identity
    Posted in the Trigonometry Forum
    Replies: 2
    Last Post: Sep 1st 2009, 07:02 AM
  4. Verify the identity:
    Posted in the Trigonometry Forum
    Replies: 2
    Last Post: Dec 15th 2008, 10:57 AM
  5. help me verify this identity
    Posted in the Trigonometry Forum
    Replies: 2
    Last Post: Jul 12th 2008, 04:52 PM

Search Tags


/mathhelpforum @mathhelpforum