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Himpunan penyelesaian cos 2x = 3 cos x - 2 untuk 0 ≤ x ≤ 2 π adalah ....

Himpunan penyelesaian cos 2x = 3 cos x - 2 untuk adalah ....
 

  1. left curly bracket 0 comma straight pi over 2 comma 3 over 2 straight pi comma space 2 straight pi right curly bracket

  2. left curly bracket 0 comma straight pi over 3 comma space 5 over 3 straight pi comma space 2 straight pi right curly bracket

  3. left curly bracket 0 comma straight pi over 3 comma space 3 over 2 straight pi comma space 2 straight pi right curly bracket

  4. left curly bracket 0 comma space straight pi over 2 comma space straight pi comma space 3 over 2 straight pi right curly bracket

  5. left curly bracket 0 comma straight pi over 2 comma straight pi comma 2 straight pi right curly bracket

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I. Roy

Master Teacher

Mahasiswa/Alumni Universitas Negeri Surabaya

Jawaban terverifikasi

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Pembahasan

cos 2 x =3 cos x - 2 cos 2 x - 3 cos x + 2=0

cos2x=3cosx - 2

cos2x - 3cosx + 2=0

left parenthesis 2 cos squared x minus 1 right parenthesis minus 3 cos x plus 2 equals 0  2 cos squared x minus 3 cos x plus 1 equals 0  left parenthesis 2 cos x minus 1 right parenthesis left parenthesis cos x minus 1 right parenthesis equals 0  cos x equals 1 half space a t a u space cos x equals 1  P e n y e l e s a i a n space I colon  cos x equals 1 half  cos x equals cos straight pi over 3  x equals straight pi over 3  cos x equals 1 half  cos x equals cos fraction numerator 5 straight pi over denominator 3 end fraction  x equals fraction numerator 5 straight pi over denominator 3 end fraction  P e n y e l e s a i a n space I I colon  cos x equals 1  cos x equals cos 0  x equals 0  d a n  cos x equals 1  cos x equals cos 2 straight pi  straight x equals 2 straight pi  Jadi space himpunan space penyelesaian space adalah

left curly bracket 0 comma straight pi over 3 comma space 5 over 3 straight pi comma space 2 straight pi right curly bracket

 

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