Pertanyaan

Hitunglah nilai dari bentuk 2 sin 2 60 − 1 cos 2 6 0 ∘ − sin 2 6 0 ∘

Hitunglah nilai dari bentuk $\frac{cos ^{2} 6 0 ^{\circ} - sin ^{2} 6 0 ^{\circ}}{2 sin ^{2} 60 - 1}$

Ikuti Tryout SNBT & Menangkan E-Wallet 100rb

Habis dalam

Klaim

D. Rajib

Master Teacher

Mahasiswa/Alumni Universitas Muhammadiyah Malang

Jawaban terverifikasi

Jawaban

nilai dari adalah

nilai dari $fraction numerator cos squared space 60 degree minus sin squared space 60 degree over denominator 2 sin squared space 60 minus 1 end fraction$ adalah negative 1

Pembahasan

Ingat kembali bahwa maka Jadi, nilai dari adalah

Ingat kembali bahwa sin squared space straight alpha plus cos squared space straight alpha equals 1 maka

$table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator cos squared space 60 degree minus sin squared space 60 degree over denominator 2 sin squared space 60 minus 1 end fraction end cell equals cell fraction numerator cos squared space 60 degree minus left parenthesis 1 minus cos squared space 60 degree right parenthesis over denominator 2 left parenthesis 1 minus cos squared space 60 degree right parenthesis minus 1 space end fraction end cell row blank equals cell fraction numerator 2 space cos squared space 60 degree minus 1 over denominator 2 minus 2 space cos space 60 degree minus 1 end fraction end cell row blank equals cell fraction numerator 2 left parenthesis begin display style 1 half end style right parenthesis squared minus 1 over denominator 1 minus 2 left parenthesis begin display style 1 half end style right parenthesis squared end fraction end cell row blank equals cell fraction numerator 2 left parenthesis begin display style 1 fourth end style right parenthesis minus 1 over denominator 1 minus 2 left parenthesis begin display style 1 fourth end style right parenthesis end fraction end cell row blank equals cell fraction numerator begin display style 1 half end style minus 1 over denominator 1 minus begin display style 1 half end style end fraction end cell row blank equals cell fraction numerator negative begin display style 1 half end style over denominator begin display style 1 half end style end fraction end cell row blank equals cell negative 1 end cell end table$

Jadi, nilai dari $fraction numerator cos squared space 60 degree minus sin squared space 60 degree over denominator 2 sin squared space 60 minus 1 end fraction$ adalah negative 1