Pertanyaan

Nilai dari cos 21 0 ∘ − cos 30 0 ∘ sin 12 0 ∘ + sin 15 0 ∘ = ⋯ cos 21 0 ∘ − cos 30 0 ∘ sin 12 0 ∘ + sin 15 0 ∘ = …

Nilai dari $\frac{sin 12 0 ^{\circ} + sin 15 0 ^{\circ}}{cos 21 0 ^{\circ} - cos 30 0 ^{\circ}} = \dots$ $\frac{sin 12 0 ^{\circ} + sin 15 0 ^{\circ}}{cos 21 0 ^{\circ} - cos 30 0 ^{\circ}} = \dots$

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Jawaban terverifikasi

Jawaban

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$begin mathsize 14px style fraction numerator sin space 120 degree plus sin space 150 degree over denominator cos space 210 degree minus cos space 300 degree end fraction equals negative 1 end style$ .

Pembahasan

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Diperoleh:

$begin mathsize 14px style fraction numerator sin space 120 degree plus sin space 150 degree over denominator cos space 210 degree minus cos space 300 degree end fraction equals midline horizontal ellipsis end style$ $table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator sin space 120 degree plus sin space 150 degree over denominator cos space 210 degree minus cos space 300 degree end fraction end cell row blank equals cell fraction numerator sin left parenthesis 180 degree minus 60 degree right parenthesis plus sin left parenthesis 180 degree minus 30 degree right parenthesis over denominator cos left parenthesis 180 degree plus 30 degree right parenthesis minus cos left parenthesis 360 degree minus 60 degree right parenthesis end fraction end cell row blank equals cell fraction numerator sin space 60 degree plus sin space 30 degree over denominator negative cos space 30 degree minus cos space 60 degree end fraction end cell row blank equals cell fraction numerator begin display style 1 half end style square root of 3 plus begin display style 1 half end style over denominator negative begin display style 1 half end style square root of 3 minus begin display style 1 half end style end fraction end cell row blank equals cell fraction numerator begin display style 1 half square root of 3 plus 1 half end style over denominator negative open parentheses begin display style 1 half end style square root of 3 plus begin display style 1 half end style close parentheses end fraction end cell row blank equals cell fraction numerator 1 over denominator negative 1 end fraction end cell row blank equals cell negative 1 end cell end table$

Jadi, $begin mathsize 14px style fraction numerator sin space 120 degree plus sin space 150 degree over denominator cos space 210 degree minus cos space 300 degree end fraction equals negative 1 end style$ .