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Math Help - solve for x algebraically

  1. #1
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    solve for x algebraically

    solve x algebraically not graphically

    3 cot (90 + x) = tan x sin x

    Thanx
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  2. #2
    Super Member wingless's Avatar
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    3\cot (90+x) = \tan x \sin x

    3\frac{\cos (90 + x)}{\sin (90 + x)} = \frac{\sin x}{\cos x} \sin x

    3\frac{-\sin x}{\cos x} = \frac{\sin^2 x}{\cos x}

    3\frac{-\sin x}{\not{\cos x}} = \frac{\sin^2 x}{\not{\cos x}}

    -3\sin x = \sin^2 x

    ......... \sin x = 0 works

    We'll try to get another answer,

    -3\not{\sin x} = \sin^{\not 2} x

    -3 = \sin x There's no solution here.

    Then we only use \sin x = 0.

    Hence, x = k\pi
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  3. #3
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    Hello, Nico!

    A slightly different approach . . .


    3\cot(90 + x) \:=\: \tan x\sin x

    Since \cot(x + 90) \:=\:-\tan x, we have:

    . . -3\tan x \:=\:\tan x\sin x \quad\Rightarrow\quad \tan x\sin x + 3\tan x \:=\:0

    Factor: . \tan x(\sin x + 3) \:=\:0


    But . \sin x + 3 \:=\:0\quad\Rightarrow\quad \sin x \:=\:-3\;\text{ has no solutions}

    Therefore: . \tan x \:=\:0\quad\Rightarrow\quad x \:=\:\pi n\:\text{ for any integer }n

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