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Pertanyaan

cos 2 1 5 ∘ − cos 2 10 5 ∘ = ...

 ...

  1. negative 1 half square root of 3

  2. negative 1 half square root of 2

  3. 0

  4. 1 half square root of 3

  5. 3 over 4

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S. Nur

Master Teacher

Jawaban terverifikasi

Jawaban

jawaban yang benar adalah D.

jawaban yang benar adalah D.

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Pembahasan

Berdasarkan rumus cosinus untuk sudut rangkap diperoleh: Dengan menggunakan rumus di atas dan aturan sudut berelasi , maka diperoleh penyelesaiannya yaitu: Jadi, . Oleh karena itu, jawaban yang benar adalah D.

Berdasarkan rumus cosinus untuk sudut rangkap diperoleh:

table attributes columnalign right center left columnspacing 0px end attributes row cell cos space 2 A end cell equals cell 2 space cos squared A minus 1 end cell row cell cos space 2 A plus 1 end cell equals cell 2 space cos squared A end cell row cell 2 space cos squared space straight A end cell equals cell 1 plus cos space 2 straight A end cell row cell cos squared space straight A end cell equals cell fraction numerator 1 plus cos space 2 straight A over denominator 2 end fraction end cell end table

Dengan menggunakan rumus di atas dan aturan sudut berelasi cos open parentheses 180 degree plus alpha close parentheses equals negative cos space alpha, maka diperoleh penyelesaiannya yaitu:

begin mathsize 12px style table attributes columnalign right center left columnspacing 0px end attributes row cell cos squared space 15 degree minus cos squared space 105 degree end cell equals cell open parentheses fraction numerator 1 plus cos space 2 times 15 degree over denominator 2 end fraction close parentheses minus open parentheses fraction numerator 1 plus cos space 2 times 105 degree over denominator 2 end fraction close parentheses end cell row blank equals cell open parentheses fraction numerator 1 plus cos space 30 degree over denominator 2 end fraction close parentheses minus open parentheses fraction numerator 1 plus cos space 210 degree over denominator 2 end fraction close parentheses end cell row blank equals cell open parentheses fraction numerator 1 plus begin display style 1 half end style square root of 3 over denominator 2 end fraction close parentheses minus open parentheses fraction numerator 1 plus cos open parentheses 180 degree plus 30 degree close parentheses over denominator 2 end fraction close parentheses end cell row blank equals cell open parentheses fraction numerator 1 plus begin display style 1 half end style square root of 3 over denominator 2 end fraction close parentheses minus open parentheses fraction numerator 1 plus open parentheses negative cos space 30 degree close parentheses over denominator 2 end fraction close parentheses end cell row blank equals cell open parentheses fraction numerator 1 plus begin display style 1 half end style square root of 3 over denominator 2 end fraction close parentheses minus open parentheses fraction numerator 1 minus begin display style 1 half end style square root of 3 over denominator 2 end fraction close parentheses end cell row blank equals cell open parentheses fraction numerator begin display style 2 over 2 plus 1 half square root of 3 end style over denominator 2 end fraction close parentheses minus open parentheses fraction numerator begin display style 2 over 2 minus 1 half square root of 3 end style over denominator 2 end fraction close parentheses end cell row blank equals cell open parentheses fraction numerator 2 plus square root of 3 over denominator 2 end fraction times 1 half close parentheses minus open parentheses fraction numerator 2 minus square root of 3 over denominator 2 end fraction times 1 half close parentheses end cell row blank equals cell fraction numerator 2 plus square root of 3 over denominator 4 end fraction minus fraction numerator open parentheses 2 minus square root of 3 close parentheses over denominator 4 end fraction end cell row blank equals cell fraction numerator 2 minus 2 plus square root of 3 plus square root of 3 over denominator 4 end fraction end cell row blank equals cell fraction numerator 2 square root of 3 over denominator 4 end fraction end cell row blank equals cell 1 half square root of 3 end cell end table end style


Jadi, cos squared space 15 degree minus cos squared space 105 degree equals1 half square root of 3.

Oleh karena itu, jawaban yang benar adalah D.

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