Pertanyaan

Himpunan penyelesaian dari persamaan cos x + 3 tan 3 0 ∘ = 2 sin 2 1 x ⋅ cos 2 1 x untuk 0 ∘ ≤ x ≤ 36 0 ∘ adalah...

Himpunan penyelesaian dari persamaan $cos x + 3 tan 3 0^{\circ} = 2 sin \frac{1}{2} x \cdot cos \frac{1}{2} x$ untuk $0^{\circ} \leq x \leq 36 0^{\circ}$ adalah...

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Habis dalam

Klaim

Z. Apriani

Master Teacher

Mahasiswa/Alumni Institut Teknologi Bandung

Jawaban terverifikasi

Jawaban

jawaban yang benar adalah D.

Pembahasan

Dengan mengggunakan rumus trigonometri, diperoleh: Misalkan, Sehingga, Kemudian, Jadi, . Oleh karena itu, jawaban yang benar adalah D.

Dengan mengggunakan rumus trigonometri, diperoleh:

$table attributes columnalign right center left columnspacing 0px end attributes row cell cos space x plus square root of 3 tan space 30 degree end cell equals cell 2 sin 1 half x times cos 1 half x end cell row cell cos space x plus square root of 3 times fraction numerator 1 over denominator square root of 3 end fraction end cell equals cell 2 sin 1 half x times cos 1 half x end cell row cell cos space x plus 1 end cell equals cell 2 sin 1 half x times cos 1 half x end cell row cell cos space x plus 1 end cell equals cell sin 2 times 1 half x end cell row cell cos space x plus 1 end cell equals cell sin x end cell row cell cos space x minus sin space x end cell equals cell negative 1 end cell end table$

Misalkan,

table attributes columnalign right center left columnspacing 0px end attributes row cell cos space x minus sin space x end cell equals cell k cos left parenthesis x plus alpha right parenthesis degree end cell row blank equals cell k cos space x degree times cos space alpha degree minus k sin space x degree times sin space alpha degree end cell end table

Sehingga,

Kemudian,

$table attributes columnalign right center left columnspacing 0px end attributes row cell k cos space left parenthesis x plus alpha right parenthesis degree end cell equals cell square root of 2 cos space left parenthesis x plus 45 right parenthesis degree equals negative 1 end cell row blank left right double arrow cell cos space left parenthesis x plus 45 right parenthesis degree equals fraction numerator negative 1 over denominator square root of 2 end fraction end cell row cell cos space left parenthesis x plus 45 right parenthesis degree end cell equals cell fraction numerator negative 1 over denominator square root of 2 end fraction end cell row cell cos space left parenthesis x plus 45 right parenthesis degree end cell equals cell cos space 135 degree end cell row cell space x plus 45 degree end cell equals cell plus-or-minus 135 degree plus n times 360 degree end cell row x equals cell 90 degree plus n times 360 degree end cell row cell untuk space n end cell equals cell 0 comma space 1 end cell row x equals cell 90 degree plus 0 times 360 degree end cell row blank equals cell 90 degree end cell row x equals cell 90 degree plus 1 times 360 degree end cell row blank equals cell 450 degree end cell row cell atau space x end cell equals cell negative 180 degree plus n times 360 degree end cell row n equals cell 0 comma space 1 end cell row x equals cell negative 180 degree plus 0 times 360 degree end cell row blank equals cell negative 180 degree end cell row x equals cell negative 180 degree plus 1 times 360 degree end cell row blank equals cell 180 degree end cell end table$

Jadi, HP equals open curly brackets 90 degree comma space 180 degree close curly brackets .

Oleh karena itu, jawaban yang benar adalah D.