Pertanyaan

Tentukan nilai dari: 2 cos 3 0 ∘ tan 6 0 ∘ sin 2 6 0 ∘ − cos 2 6 0 ∘

Tentukan nilai dari:

$\frac{sin ^{2} 6 0 ^{\circ} - cos ^{2} 6 0 ^{\circ}}{2 cos 3 0 ^{\circ} tan 6 0 ^{\circ}}$

L. Rante

Master Teacher

Mahasiswa/Alumni Universitas Negeri Makassar

Jawaban terverifikasi

Jawaban

.

$fraction numerator sin squared space 60 degree minus cos squared space 60 degree over denominator 2 space cos space 30 degree space tan space 60 degree end fraction equals 1 over 6$ .

Pembahasan

Berdasarkan tebel trigonometri sudut istimewa diperoleh Maka Jadi, .

Berdasarkan tebel trigonometri sudut istimewa diperoleh

table attributes columnalign right center left columnspacing 0px end attributes row cell sin space 60 degree end cell equals cell 1 half square root of 3 end cell row cell cos space 60 degree end cell equals cell 1 half end cell row cell cos space 30 degree end cell equals cell 1 half square root of 3 end cell row cell tan space 60 degree end cell equals cell square root of 3 end cell end table

Maka

$table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator sin squared space 60 degree minus cos squared space 60 degree over denominator 2 space cos space 30 degree space tan space 60 degree end fraction end cell equals cell fraction numerator open parentheses begin display style 1 half end style square root of 3 close parentheses squared minus open parentheses begin display style 1 half end style close parentheses squared over denominator 2 times open parentheses begin display style 1 half end style square root of 3 close parentheses times open parentheses square root of 3 close parentheses end fraction end cell row blank equals cell fraction numerator begin display style 3 over 4 end style minus begin display style 1 fourth end style over denominator 3 end fraction end cell row blank equals cell fraction numerator begin display style 2 over 4 end style over denominator 3 end fraction end cell row blank equals cell 1 over 6 end cell end table$

Jadi, $fraction numerator sin squared space 60 degree minus cos squared space 60 degree over denominator 2 space cos space 30 degree space tan space 60 degree end fraction equals 1 over 6$ .