Pertanyaan

Himpunan penyelesaian persamaan cos x 1 + sin x + 1 + sin x cos x = 4 untuk 0 ≤ x ≤ 2 π adalah ….

Himpunan penyelesaian persamaan $\frac{1 + sin x}{cos x} + \frac{cos x}{1 + sin x} = 4$ untuk $0 \leq x \leq 2 π$ adalah ….

$begin mathsize 14px style open curly brackets straight pi over 3 comma fraction numerator 5 straight pi over denominator 3 end fraction close curly brackets end style$
$begin mathsize 14px style open curly brackets straight pi over 3 comma fraction numerator 4 straight pi over denominator 3 end fraction close curly brackets end style$
$begin mathsize 14px style open curly brackets 0 comma fraction numerator 5 straight pi over denominator 3 end fraction comma straight 2 straight pi close curly brackets end style$
$begin mathsize 14px style open curly brackets fraction numerator 3 straight pi over denominator 2 end fraction comma fraction numerator 5 straight pi over denominator 3 end fraction close curly brackets end style$

I. Sutiawan

Master Teacher

Mahasiswa/Alumni Universitas Pasundan

Jawaban terverifikasi

Jawaban

himpunan penyelesaian persamaan tersebut adalah

Pembahasan

Gunakan rumus penjumlahan sin berikut ini : Maka, Kemungkinan pertama: Kemungkinan pertama: Jadi himpunan penyelesaian persamaan tersebut adalah

Gunakan rumus penjumlahan sin berikut ini :

$begin mathsize 14px style sin space straight A plus sin space straight B equals 2 space sin space open parentheses fraction numerator straight A plus straight B over denominator 2 end fraction close parentheses space cos space open parentheses fraction numerator straight A minus straight B over denominator 2 end fraction close parentheses end style$

Maka,

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator 1 plus sin space straight x over denominator cos space straight x end fraction plus fraction numerator cos space straight x over denominator 1 plus sin space straight x end fraction end cell equals 4 row cell fraction numerator open parentheses 1 plus sin space straight x close parentheses squared plus cos squared space straight x over denominator cos space straight x open parentheses 1 plus sin space straight x close parentheses end fraction end cell equals 4 row cell fraction numerator 1 plus 2 space sin space straight x plus sin squared space straight x plus cos squared space straight x over denominator cos space straight x space open parentheses 1 plus sin space straight x close parentheses end fraction end cell equals 4 row cell fraction numerator 1 plus 2 space sin space straight x plus 1 over denominator cos space straight x space open parentheses 1 plus sin space straight x close parentheses end fraction end cell equals 4 row cell fraction numerator 2 open parentheses 1 plus sin space straight x close parentheses over denominator cos space straight x space open parentheses 1 plus sin space straight x close parentheses end fraction end cell equals 4 row cell fraction numerator 2 over denominator cos space straight x end fraction end cell equals 4 row cell 2 over 4 end cell equals cell cos space straight x end cell row cell 1 half end cell equals cell cos space straight x end cell end table end style$

Kemungkinan pertama:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell cos space straight pi over 3 end cell equals cell cos space straight x end cell row cell straight pi over 3 end cell equals straight x end table end style

Kemungkinan pertama:

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell cos fraction numerator 5 straight pi over denominator 3 end fraction end cell equals cell cos space straight x end cell row cell fraction numerator 5 straight pi over denominator 3 end fraction end cell equals straight x end table end style$

Jadi himpunan penyelesaian persamaan tersebut adalah