Pertanyaan

Nilai dari cos 7 5 ∘ − cos 1 5 ∘ sin 10 5 ∘ − sin 1 5 ∘ adalah ....

$Nilai dari \frac{sin 10 5 ^{\circ} - sin 1 5 ^{\circ}}{cos 7 5 ^{\circ} - cos 1 5 ^{\circ}} adalah ....$

F. Pratama

Master Teacher

Mahasiswa/Alumni Universitas Putra Indonesia YPTK Padang

Jawaban terverifikasi

Pembahasan

$sin space A space minus space sin space B space equals space 2 space cos open parentheses fraction numerator A plus B over denominator 2 end fraction close parentheses space sin open parentheses fraction numerator A minus B over denominator 2 end fraction close parentheses cos space A space minus space cos space B space equals space minus 2 space sin open parentheses fraction numerator A plus B over denominator 2 end fraction close parentheses space sin open parentheses fraction numerator A minus B over denominator 2 end fraction close parentheses fraction numerator sin space 105 degree space minus space sin space 15 degree over denominator cos space 75 degree space minus space cos space 15 degree end fraction space equals space fraction numerator 2 space cos open parentheses begin display style fraction numerator 105 degree thin space plus space 15 degree over denominator 2 end fraction end style close parentheses space sin open parentheses begin display style fraction numerator 105 degree minus 15 degree over denominator 2 end fraction end style close parentheses over denominator negative 2 space sin open parentheses begin display style fraction numerator 75 degree plus 15 degree over denominator 2 end fraction end style close parentheses space sin open parentheses begin display style fraction numerator 75 degree minus 15 degree over denominator 2 end fraction end style close parentheses end fraction space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals space fraction numerator 2 space cos space 60 space sin space 45 over denominator negative 2 space sin space 45 space sin space 30 end fraction space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals space minus fraction numerator cos space 60 over denominator sin space 30 end fraction space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals space minus fraction numerator begin display style 1 half end style over denominator begin display style 1 half end style end fraction space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals space minus 1$