Pertanyaan

Nilai dari cos 30 − tan 3 0 ∘ sin 6 0 ∘ + cos 4 5 ∘ = ⋯

Nilai dari $\frac{sin 6 0 ^{\circ} + cos 4 5 ^{\circ}}{cos 30 - tan 3 0 ^{\circ}} = \dots$

Ikuti Tryout SNBT & Menangkan E-Wallet 100rb

Habis dalam

Klaim

A. Acfreelance

Master Teacher

Jawaban terverifikasi

Pembahasan

Ingat nilai trigonometri untuk sudut sudut spesial. Nah, tinggal kita gunakan saja nilai-nilainya ya yang sesuai pertama-tama kita sederhanakan dulu ya, penyebutnya dan pembilangnya Jadi...

Ingat nilai trigonometri untuk sudut sudut spesial.

$sin space 30 degree equals 1 half space space space space cos space 30 degree equals fraction numerator square root of 3 over denominator 2 end fraction space space space space tan space 30 degree equals fraction numerator 1 over denominator square root of 3 end fraction space space space space space sin space 45 degree equals fraction numerator square root of 2 over denominator 2 end fraction space space space space cos space 45 degree equals fraction numerator square root of 2 over denominator 2 end fraction space space space space tan space 45 degree equals 1 space space space space space sin space 60 degree equals fraction numerator square root of 3 over denominator 2 end fraction space space space space cos space 60 degree equals 1 half space space space space tan space 60 degree equals square root of 3 space space space space space$

Nah, tinggal kita gunakan saja nilai-nilainya ya yang sesuai

undefined

pertama-tama kita sederhanakan dulu ya,

penyebutnya $fraction numerator square root of 3 over denominator 2 end fraction plus fraction numerator square root of 2 over denominator 2 end fraction equals 1 half open parentheses square root of 3 plus square root of 2 close parentheses$

dan pembilangnya $fraction numerator square root of 3 over denominator 2 end fraction minus fraction numerator square root of 3 over denominator 3 end fraction equals square root of 3 space open parentheses 1 half minus 1 third close parentheses space equals space square root of 3 space open parentheses 3 over 6 minus 2 over 6 close parentheses space equals space space square root of 3 space open parentheses 1 over 6 close parentheses equals fraction numerator square root of 3 over denominator 6 end fraction$

Jadi...

$equals fraction numerator fraction numerator square root of 3 plus square root of 2 over denominator 2 end fraction over denominator fraction numerator square root of 3 over denominator 6 end fraction end fraction equals fraction numerator 6 left parenthesis square root of 3 plus square root of 2 right parenthesis over denominator 2 left parenthesis square root of 3 right parenthesis end fraction. fraction numerator square root of 3 over denominator square root of 3 end fraction equals fraction numerator 6 left parenthesis 3 plus square root of 6 right parenthesis over denominator 6 end fraction equals 3 plus square root of 6$