Find all solutions of each equation on the interval [0, 2pi) (cos^3x)/(sinx )=cot x

Question

Find all solutions of each equation on the interval [0, 2pi)

(cos^3x)/(sinx )=cot x

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Eirian 4 years 2021-08-27T09:16:45+00:00 1 Answers 11 views 0

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  1. Nick
    0
    2021-08-27T09:18:20+00:00
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    Answer:

    Step-by-step explanation:

    (cos³x)/(sin x)=cot x

    (cos³ x)/(sin x)=(cos x)/sin x

    sin x≠0

    x≠0,π,2π

    cos³x-cos x=0

    cos x(cos²x-1)=0

    either cos x=0,x=π/2 ,3π/2

    or

    cos²x-1=0

    2 cos²x=2

    1+cos 2x=2

    cos 2x=1=cos2nπ,n=0,1,2

    2x=2nπ

    x=nπ

    x=0,π,2π

    But x≠0,π,2π

    so x=π/2,3π/2

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