Solve over the interval [0,2π) 2(cos^2)x+cosx=0

Mylo O'Moore

Mylo O'Moore

Answered question

2021-02-05

Solve over the interval

[0,2π)2(cos2)x+cosx=0

Answer & Explanation

Pohanginah

Pohanginah

Skilled2021-02-06Added 96 answers

The terms of 2(cos2)x+cosx=0 have a common factor of cosx. Factoring out cosx then gives cosx(2cosx+1)=0.
The Zero Product Property states that if ab=0, then a=0 or b=0. Therefore, if cosx(2cosx+1)=0, then cosx=0 or 2cosx+1=0.
From the unit circle, cosx=0 when x=1

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