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Jika x=sin 3θ +sin θ dan y=cos 3θ +cos θ, maka nilai x2−y2=...

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Jika straight x equals sin space 3 straight theta space plus sin space straight theta space dan space straight y equals cos space 3 straight theta space plus cos space straight theta, maka nilai straight x squared minus straight y squared equals...

  1. cos space 2 straight theta

  2. 1 plus table attributes columnalign right center left columnspacing 0px end attributes row blank blank cos end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 2 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank straight theta end table

  3. 2 minus table attributes columnalign right center left columnspacing 0px end attributes row blank blank cos end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 2 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank straight theta end table

  4. table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 2 plus 2 space cos space 2 straight theta end cell end table

  5. table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell sin space 2 straight theta plus cos space 2 straight theta end cell end table

I. Rachmawati

Master Teacher

Mahasiswa/Alumni Universitas Negeri Malang

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah D.

Pembahasan

Ingat kembali:

  1. rumus rumus perbandingan trigonometri untuk selisih dua sudut: cos space left parenthesis straight A minus straight B right parenthesis equals table attributes columnalign right center left columnspacing 0px end attributes row blank blank sin end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank straight A end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank sin end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank straight B end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank plus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cos end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank straight A end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cos end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank straight B end table.
  2. identitas: sin squared space straight A plus cos squared space straight A equals 1

Diketahui straight x equals sin space 3 straight theta space plus sin space straight theta space dan space straight y equals cos space 3 straight theta space plus cos space straight theta, maka penyelesaian soal di atas adalah

table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell straight x squared plus straight y squared end cell row blank equals cell open parentheses sin space 3 straight theta space plus sin space straight theta close parentheses squared space plus open parentheses cos space 3 straight theta space plus cos space straight theta close parentheses squared end cell row blank equals cell sin to the power of 2 space end exponent 3 straight theta space plus space 2 space sin space 3 straight theta space sin space straight theta space plus sin squared space straight theta space plus left parenthesis cos squared space 3 straight theta space plus 2 space cos space 3 straight theta space cos space straight theta plus cos squared space straight theta right parenthesis end cell row blank equals cell open parentheses sin to the power of 2 space end exponent 3 straight theta plus cos squared space 3 straight theta close parentheses plus open parentheses sin squared space straight theta space plus cos squared space straight theta close parentheses plus 2 open parentheses sin space 3 straight theta space sin space straight theta plus cos space 3 straight theta space cos space straight theta close parentheses end cell row blank equals cell 1 plus 1 plus 2 space cos space left parenthesis 3 straight theta minus straight theta right parenthesis end cell row blank equals cell 2 plus 2 space cos space 2 straight theta end cell end table  

Jadi, table attributes columnalign right center left columnspacing 0px end attributes row cell straight x squared plus straight y squared end cell equals cell 2 plus 2 space cos space 2 straight theta end cell end table.

Oleh karena itu, jawaban yang tepat adalah D.

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