Pertanyaan

cos 1 0 ∘ + cos 2 0 ∘ + cos 4 0 ∘ + cos 5 0 ∘ sin 1 0 ∘ + sin 2 0 ∘ + sin 4 0 ∘ + sin 5 0 ∘ = ...

$\frac{sin 1 0 ^{\circ} + sin 2 0 ^{\circ} + sin 4 0 ^{\circ} + sin 5 0 ^{\circ}}{cos 1 0 ^{\circ} + cos 2 0 ^{\circ} + cos 4 0 ^{\circ} + cos 5 0 ^{\circ}} = ...$

Ikuti Tryout SNBT & Menangkan E-Wallet 100rb

Habis dalam

Klaim

N. Sari

Master Teacher

Mahasiswa/Alumni Universitas Nasional

Jawaban terverifikasi

Jawaban

jawaban yang benar adalah C.

Pembahasan

Sifat penjumlahan dan pengurangan trigonometri : Sifat perkalian trigonometri : Dengan menggunakan sifat tersebut, maka : Maka pembilangnya : Serta, Penyebut : Serta, Maka : Maka, . Oleh karena itu, jawaban yang benar adalah C.

Sifat penjumlahan dan pengurangan trigonometri :

Sifat perkalian trigonometri :

Dengan menggunakan sifat tersebut, maka :

$fraction numerator sin space 10 degree plus sin space 20 degree plus sin space 40 degree plus sin space 50 degree over denominator cos space 10 degree plus cos space 20 degree plus cos space 40 degree plus cos space 50 degree end fraction equals fraction numerator open parentheses sin space 10 degree plus sin space 50 degree close parentheses plus open parentheses sin space 40 degree plus sin space 20 degree close parentheses over denominator open parentheses cos space 10 degree plus cos space 50 degree close parentheses plus open parentheses cos space 40 degree plus cos space 20 degree close parentheses end fraction$

Maka pembilangnya :

sin space 10 degree plus sin space 50 degree equals sin space 50 degree plus sin space 10 degree equals 2 sin 1 half open parentheses 50 plus 10 close parentheses cos 1 half open parentheses 50 minus 10 close parentheses equals 2 sin space 30 degree space cos space 20 degree equals 2 cross times 1 half space cos space 20 degree equals cos space 20 degree

Serta,

sin space 40 degree plus sin space 20 degree equals 2 sin 1 half open parentheses 40 plus 20 close parentheses cos 1 half open parentheses 40 minus 20 close parentheses equals 2 sin space 30 degree space cos space 10 degree equals 2 cross times 1 half space cos space 10 degree equals cos space 10 degree

Penyebut :

Serta,

cos space 40 degree plus cos space 20 degree equals 2 cos 1 half open parentheses 40 plus 20 close parentheses cos 1 half open parentheses 40 minus 20 close parentheses equals 2 cos space 30 degree space cos space 10 degree equals 2 cross times 1 half square root of 3 space cos space 10 degree equals square root of 3 space cos space 10 degree

Maka :

$fraction numerator sin space 10 degree plus sin space 20 degree plus sin space 40 degree plus sin space 50 degree over denominator cos space 10 degree plus cos space 20 degree plus cos space 40 degree plus cos space 50 degree end fraction equals fraction numerator cos space 20 plus cos space 10 over denominator square root of 3 cos space 20 plus square root of 3 space cos space 10 end fraction equals fraction numerator 1 over denominator square root of 3 end fraction equals 1 third square root of 3$

Maka, $fraction numerator sin space 10 degree plus sin space 20 degree plus sin space 40 degree plus sin space 50 degree over denominator cos space 10 degree plus cos space 20 degree plus cos space 40 degree plus cos space 50 degree end fraction equals 1 third square root of 3$ .

Oleh karena itu, jawaban yang benar adalah C.