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Pertanyaan

Hasil dari fraction numerator sin space open parentheses 60 minus a close parentheses degree plus sin space open parentheses sin space 60 plus a close parentheses degree over denominator cos space open parentheses 30 plus a close parentheses degree plus cos space open parentheses 30 minus a close parentheses degree end fraction equals...

  1. negative square root of 3

  2. negative 1 third square root of 3

  3. 1 third square root of 3

  4. 1

  5. square root of 3

D. Nuryani

Master Teacher

Mahasiswa/Alumni Universitas Padjadjaran

Jawaban terverifikasi

Jawaban

jawaban yang benar adalah D.

Pembahasan

Ingat kembali rumus-rumus penjumlahan sinus dan penjumlahan cosinus berikut.

  1. sin space alpha plus sin space beta equals 2 space sin space open parentheses fraction numerator alpha plus beta over denominator 2 end fraction close parentheses space cos space open parentheses fraction numerator alpha minus beta over denominator 2 end fraction close parentheses
  2. cos space alpha plus cos space beta equals 2 space cos space open parentheses fraction numerator alpha plus beta over denominator 2 end fraction close parentheses space cos space open parentheses fraction numerator alpha minus beta over denominator 2 end fraction close parentheses

Berdasarkan rumus-rumus di atas, maka:

table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator sin space open parentheses 60 minus a close parentheses degree plus sin space open parentheses sin space 60 plus a close parentheses degree over denominator cos space open parentheses 30 plus a close parentheses degree plus cos space open parentheses 30 minus a close parentheses degree end fraction end cell row blank equals cell fraction numerator up diagonal strike 2 space sin space open parentheses begin display style fraction numerator open parentheses 60 minus a plus 60 plus a close parentheses degree over denominator 2 end fraction end style close parentheses space cos space open parentheses begin display style fraction numerator open parentheses 60 minus a minus 60 minus a close parentheses degree over denominator 2 end fraction end style close parentheses over denominator up diagonal strike 2 space cos space open parentheses begin display style fraction numerator open parentheses 30 plus a plus 30 minus a close parentheses degree over denominator 2 end fraction end style close parentheses space cos space open parentheses begin display style fraction numerator open parentheses 30 plus a minus 30 plus a close parentheses degree over denominator 2 end fraction end style close parentheses end fraction end cell row blank equals cell fraction numerator sin space 60 degree times cos open parentheses negative a close parentheses degree over denominator cos space 30 degree times cos space a degree end fraction end cell row blank equals cell fraction numerator sin space 60 degree times up diagonal strike cos space a degree end strike over denominator cos space 30 degree times up diagonal strike cos space a degree end strike end fraction end cell row blank equals cell fraction numerator begin display style 1 half end style square root of 3 over denominator begin display style 1 half end style square root of 3 end fraction end cell row blank equals 1 end table

Dengan demikian, nilai dari fraction numerator sin space open parentheses 60 minus a close parentheses degree plus sin space open parentheses sin space 60 plus a close parentheses degree over denominator cos space open parentheses 30 plus a close parentheses degree plus cos space open parentheses 30 minus a close parentheses degree end fraction adalah 1.

Oleh karena itu, jawaban yang benar adalah D.

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