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Pertanyaan

sin squared space 3 x space sin space 5 x sama dengan ... .

  1. 1 fourth open parentheses sin space x plus 2 space sin space 5 x plus sin space 11 x close parentheses

  2. 1 fourth open parentheses sin space x plus 2 space sin space 5 x minus sin space 11 x close parentheses

  3. 1 fourth open parentheses sin space x minus 2 space sin space 5 x plus sin space 11 x close parentheses

  4. 1 half open parentheses sin space x minus 2 space sin space 5 x plus sin space 11 x close parentheses

  5. 1 half open parentheses sin space x plus 2 space sin space 5 x minus sin space 11 x close parentheses

L. Nikmah

Master Teacher

Mahasiswa/Alumni Universitas Pendidikan Indonesia

Jawaban terverifikasi

Jawaban

jawaban yang benar adalah B.

Pembahasan

 

Ingat rumus perkalian trigonometri berikut ini:

2 space sin space A space sin space B space equals negative cos space left parenthesis A plus B right parenthesis plus cos space left parenthesis A – B right parenthesis

2 space sin space A space cos space B equals sin space left parenthesis A plus B right parenthesis plus sin space left parenthesis A – B right parenthesis dan 

2 space cos space A space sin space B equals sin space left parenthesis A plus B right parenthesis – sin space left parenthesis A – B right parenthesis

Dengan menggunakan rumus tersebut, diperoleh:

table attributes columnalign right center left columnspacing 0px end attributes row cell sin squared space 3 x space sin space 5 x end cell equals cell sin space 3 x space sin space 3 x space sin space 5 x end cell row blank equals cell sin space 3 x space sin space 5 x space sin space 3 x space end cell row blank equals cell sin space 3 x space open parentheses sin space 5 x space sin space 3 x close parentheses space end cell row blank equals cell sin space 3 x space 1 half open square brackets negative cos space open parentheses 5 x plus 3 x close parentheses plus cos space open parentheses 5 x minus 3 x close parentheses close square brackets end cell row blank equals cell sin space 3 x space 1 half open square brackets negative cos space 8 x plus cos space 2 x close square brackets end cell row blank equals cell 1 half open square brackets negative cos space 8 x space sin space 3 x plus sin space 3 x space cos space 2 x close square brackets end cell row blank equals cell 1 half open curly brackets negative 1 half open square brackets sin space open parentheses space 8 x plus 3 x close parentheses space sin space open parentheses 8 x minus 3 x close parentheses close square brackets plus 1 half open square brackets sin space open parentheses 3 x plus 2 x close parentheses plus sin space open parentheses 3 x minus 2 x close parentheses close square brackets close curly brackets end cell row blank equals cell 1 half open square brackets negative 1 half open parentheses sin space 11 x space minus space sin space 5 x close parentheses plus 1 half open parentheses sin space 5 x plus sin space x close parentheses close square brackets end cell row blank equals cell 1 half open square brackets 1 half open parentheses negative sin space 11 x plus sin space 5 x plus sin space 5 x plus sin space x close parentheses close square brackets end cell row blank equals cell 1 half open square brackets 1 half open parentheses negative sin space 11 x plus 2 space sin space 5 x plus sin space x close parentheses close square brackets end cell row blank equals cell 1 half open square brackets 1 half open parentheses sin space x plus 2 space sin space 5 x minus sin space 11 x close parentheses close square brackets end cell row blank equals cell 1 fourth open parentheses sin space x plus 2 space sin space 5 x minus sin space 11 x close parentheses end cell end table

Jadi, sin squared space 3 x space sin space 5 x space table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 1 fourth end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open parentheses sin space x plus 2 space sin space 5 x minus sin space 11 x close parentheses end cell end table.

Oleh karena itu, jawaban yang benar adalah B.

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