Pertanyaan

Sederhanakan: cos 6 0 ∘ ⋅ cos 1 5 ∘ ⋅ cos 2 5 ∘ sin 4 5 ∘ ⋅ sin 6 5 ∘ ⋅ sin 7 5 ∘

Sederhanakan: $\frac{sin 4 5 ^{\circ} \cdot sin 6 5 ^{\circ} \cdot sin 7 5 ^{\circ}}{cos 6 0 ^{\circ} \cdot cos 1 5 ^{\circ} \cdot cos 2 5 ^{\circ}}$

S. Nur

Master Teacher

Jawaban terverifikasi

Jawaban

Pembahasan

Bentuk sederhana dari operasi tersebut adalah sebagai berikut. Dengan demikian,

Bentuk sederhana dari operasi tersebut adalah sebagai berikut.

$table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator sin space 45 degree times sin space 65 degree times sin space 75 degree over denominator cos space 60 degree times cos space 15 degree times cos space 25 degree end fraction end cell row blank equals cell fraction numerator sin space 45 degree times sin space open parentheses 90 degree minus 25 degree close parentheses times sin space open parentheses 90 degree minus 15 degree close parentheses over denominator cos space 60 degree times cos space 15 degree times cos space 25 degree end fraction end cell row blank equals cell fraction numerator sin space 45 degree times cos space 25 degree times cos space 15 degree over denominator cos space 60 degree times cos space 15 degree times cos space 25 degree end fraction end cell row blank equals cell fraction numerator sin space 45 degree over denominator cos space 60 degree end fraction end cell row blank equals cell fraction numerator begin display style 1 half end style square root of 2 over denominator begin display style 1 half end style end fraction end cell row blank equals cell square root of 2 end cell end table$

Dengan demikian, $table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator sin space 45 degree times sin space 65 degree times sin space 75 degree over denominator cos space 60 degree times cos space 15 degree times cos space 25 degree end fraction end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell square root of 2 end cell end table$