16. Buktikan. a. cos 4x+cos 2xsin 4x+sin 2x=tan 3x

Pertanyaan

16. Buktikan.

a. $fraction numerator sin space 4 x plus sin space 2 x over denominator cos space 4 x plus cos space 2 x end fraction equals tan space 3 x$

P. Tessalonika

Master Teacher

Mahasiswa/Alumni Universitas Negeri Medan

Jawaban terverifikasi

Pembahasan

Ingat rumus identitas penjumlahan sinus dan cosinus berikut:

Dari soal diketahui:

x = 4x

y = 2x

Sehingga persamaan trigonometri tersebut menjadi:

$table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator sin space 4 x plus sin space 2 x over denominator cos space 4 x plus cos space 2 x end fraction end cell equals cell fraction numerator up diagonal strike 2 space sin space begin display style 1 half end style open parentheses 4 x plus 2 x close parentheses space up diagonal strike cos space begin display style 1 half end style open parentheses 4 x minus 2 x close parentheses end strike over denominator up diagonal strike 2 space cos space begin display style 1 half end style open parentheses 4 x plus 2 x close parentheses space up diagonal strike cos space begin display style 1 half end style open parentheses 4 x minus 2 x close parentheses end strike end fraction end cell row blank equals cell fraction numerator sin space begin display style 1 half end style open parentheses 6 x close parentheses over denominator cos space begin display style 1 half end style open parentheses 6 x close parentheses end fraction end cell row blank equals cell fraction numerator sin space 3 x over denominator cos space 3 x end fraction end cell row blank equals cell tan space 3 x end cell end table$

Dengan demikian,

terbukti bahwa $fraction numerator sin space 4 x plus sin space 2 x over denominator cos space 4 x plus cos space 2 x end fraction equals tan space 3 x$ .