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Thread: Verify trigonometric identity

  1. #1
    Junior Member
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    Unreals
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    Verify trigonometric identity

    Hi!

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

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



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

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

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

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

    \frac1{\text{sin}x} \equiv \csc
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  2. #2
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    Lexington, MA (USA)
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    Re: Verify trigonometric identity

    Hello, Unreal

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


    \text{Prove: }\:\cos x(\cot x + \tan x) \:=\: \csc x
    \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}

    . . . . . . . . . . =\;\;\cos x\cdot\frac{1}{\sin x\cos x} \;\;=\;\;\frac{1}{\sin x} \;\;=\;\; \csc x
    Thanks from Unreal
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