Pertanyaan

Nilai dari cos 17 4 ∘ + cos 12 6 ∘ sin 8 4 ∘ + sin 3 6 ∘ adalah …

Nilai dari $\frac{sin 8 4 ^{\circ} + sin 3 6 ^{\circ}}{cos 17 4 ^{\circ} + cos 12 6 ^{\circ}}$ adalah …

Y. Fathoni

Master Teacher

Mahasiswa/Alumni Universitas Negeri Yogyakarta.

Jawaban terverifikasi

Pembahasan

$fraction numerator sin space 84 degree plus sin space 36 degree over denominator cos space 174 degree plus cos space 126 degree end fraction equals fraction numerator 2 space sin begin display style 1 half end style left parenthesis 84 degree plus 36 degree right parenthesis space cos begin display style 1 half end style open parentheses 84 degree minus 36 degree close parentheses over denominator 2 space cos begin display style 1 half end style open parentheses 174 degree plus 126 degree close parentheses space cos begin display style 1 half end style open parentheses 174 degree minus 126 degree close parentheses end fraction equals fraction numerator 2 space sin space open parentheses begin display style fraction numerator 120 degree over denominator 2 end fraction end style close parentheses space cos space open parentheses begin display style fraction numerator 48 degree over denominator 2 end fraction end style close parentheses over denominator 2 space cos space open parentheses begin display style fraction numerator 300 degree over denominator 2 end fraction end style close parentheses space cos space open parentheses begin display style fraction numerator 48 degree over denominator 2 end fraction end style close parentheses end fraction equals fraction numerator up diagonal strike 2 space sin space left parenthesis 60 degree right parenthesis space up diagonal strike cos space left parenthesis 24 degree right parenthesis end strike over denominator up diagonal strike 2 space cos space left parenthesis 150 degree right parenthesis space up diagonal strike cos space left parenthesis 24 degree right parenthesis end strike end fraction equals fraction numerator sin space left parenthesis 60 degree right parenthesis over denominator space cos space left parenthesis 180 degree minus 150 degree right parenthesis end fraction equals fraction numerator sin space left parenthesis 60 degree right parenthesis over denominator negative space cos space left parenthesis 30 degree right parenthesis end fraction equals fraction numerator begin display style up diagonal strike 1 half square root of 3 end strike end style over denominator negative up diagonal strike 1 half square root of 3 end strike end fraction equals negative 1$