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Hitunglah tanpa menggunakan kalkulator atau tabel trigonometri: b. cos 1 2 ∘ cos 2 4 ∘ cos 3 6 ∘ cos 4 8 ∘ cos 6 0 ∘ cos 7 2 ∘ cos 8 4 ∘

Hitunglah tanpa menggunakan kalkulator atau tabel trigonometri:

b. $cos 1 2^{\circ} cos 2 4^{\circ} cos 3 6^{\circ} cos 4 8^{\circ} cos 6 0^{\circ} cos 7 2^{\circ} cos 8 4^{\circ}$

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S. Nur

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Jawaban terverifikasi

Jawaban

diperoleh hasilnya adalah .

diperoleh hasilnya adalah 1 over 128

Pembahasan

Dengan menggunakan rumus sudut rangkap , maka Jadi, diperoleh hasilnya adalah .

Dengan menggunakan rumus sudut rangkap sin space 2 A equals 2 space sin space A thin space cos space A , maka

$begin mathsize 12px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator open square brackets 2 sin space 12 degree cos space 12 degree close square brackets space cos space 24 degree space cos space 36 degree space cos space 48 degree space open parentheses begin display style 1 half end style close parentheses space cos space 72 degree space cos space 84 degree over denominator 2 sin space 12 end fraction end cell row blank equals cell fraction numerator open square brackets 2 sin space 24 degree space cos space 24 degree close square brackets space cos space 36 degree space cos space 48 degree space cos space 72 degree space cos space 84 degree over denominator 2 times 4 space sin space 12 degree end fraction end cell row blank equals cell fraction numerator open square brackets 2 sin space 48 degree space space cos space 48 degree space close square brackets cos space 36 degree space cos space 60 degree space cos space 72 degree space cos space 84 degree over denominator 2 times 8 space sin space 12 degree end fraction end cell row blank equals cell fraction numerator sin space 96 degree space cos space 36 degree space cos space 72 degree space cos space 84 degree over denominator 16 space sin space 12 degree end fraction end cell row blank equals cell fraction numerator open square brackets 2 sin space 36 degree space cos space 36 degree close square brackets space sin left parenthesis 90 plus 6 right parenthesis degree space cos space 72 degree space cos space left parenthesis 90 minus 6 right parenthesis degree over denominator 2 sin space 36 degree space 16 space sin space 12 degree end fraction end cell row blank equals cell fraction numerator open square brackets sin space 72 degree space cos space 72 degree close square brackets space cos space 6 degree space sin space 6 degree over denominator 32 space sin space 36 degree space sin space 12 degree end fraction end cell row blank equals cell fraction numerator begin display style 1 half end style sin space 144 degree space begin display style 1 half end style sin space 12 degree over denominator 32 space sin space 36 degree space sin space 12 degree end fraction end cell row blank equals cell fraction numerator sin space left parenthesis 180 degree minus 36 degree right parenthesis over denominator 128 space sin space 36 degree end fraction end cell row blank equals cell 1 over 128 end cell row blank blank blank end table end style$

Jadi, diperoleh hasilnya adalah .