Pertanyaan

Tentukan nilai dari sin 3 0 ∘ cos 6 0 ∘ tan 2 3 0 ∘ sin 2 6 0 ∘ + tan 2 6 0 ∘ cos 2 3 0 ∘

Tentukan nilai dari $\frac{tan ^{2} 3 0 ^{\circ} sin ^{2} 6 0 ^{\circ} + tan ^{2} 6 0 ^{\circ} cos ^{2} 3 0 ^{\circ}}{sin 3 0 ^{\circ} cos 6 0 ^{\circ}}$ $\;$

D. Rajib

Master Teacher

Mahasiswa/Alumni Universitas Muhammadiyah Malang

Jawaban terverifikasi

Jawaban

nilai adalah

nilai $begin mathsize 14px style fraction numerator tan squared space 30 degree sin squared space 60 degree plus tan squared space 60 degree cos squared space 30 degree over denominator sin space 30 degree cos space 60 degree end fraction end style$ adalah begin mathsize 14px style 3 1 third end style

begin mathsize 14px style 3 1 third end style

Pembahasan

Jadi, nilai adalah

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator tan squared space 30 degree space sin squared space 60 degree plus tan squared space 60 degree cos squared space 30 degree over denominator sin space 30 degree cos space 60 degree end fraction end cell row blank equals cell fraction numerator left parenthesis begin display style 1 third end style square root of 3 right parenthesis squared times left parenthesis begin display style 1 half end style right parenthesis squared plus left parenthesis square root of 3 right parenthesis squared times left parenthesis begin display style 1 half end style square root of 3 right parenthesis squared over denominator begin display style 1 half end style times begin display style 1 half end style end fraction end cell row blank equals cell fraction numerator left parenthesis begin display style 1 third end style times begin display style 1 fourth end style right parenthesis plus left parenthesis 3 times begin display style 3 over 4 end style right parenthesis over denominator begin display style 1 fourth end style end fraction end cell row blank equals cell fraction numerator left parenthesis begin display style 1 over 12 end style plus begin display style 9 over 4 end style right parenthesis over denominator begin display style 1 fourth end style end fraction end cell row blank equals cell fraction numerator left parenthesis begin display style fraction numerator 1 plus 27 over denominator 12 end fraction end style right parenthesis over denominator begin display style 1 fourth end style end fraction end cell row blank equals cell 28 over 12 times 4 over 1 end cell row blank equals cell 28 over 3 end cell row blank equals cell 3 1 third end cell row blank blank blank end table end style$

Jadi, nilai $begin mathsize 14px style fraction numerator tan squared space 30 degree sin squared space 60 degree plus tan squared space 60 degree cos squared space 30 degree over denominator sin space 30 degree cos space 60 degree end fraction end style$ adalah begin mathsize 14px style 3 1 third end style