Pertanyaan

a. Buktikanlah: sin 5 4 ∘ − sin 1 8 ∘ = 2 1 ( Petunjuk : Ruas kiri kalikan dengan 2 cos 1 8 ∘ 2 cos 1 8 ∘ )

a. Buktikanlah: $sin 5 4^{\circ} - sin 1 8^{\circ} = \frac{1}{2}$
(Petunjuk: Ruas kiri kalikan dengan $\frac{2 cos 1 8 ^{\circ}}{2 cos 1 8 ^{\circ}}$ )

S. Nur

Master Teacher

Jawaban terverifikasi

Jawaban

Terbukti bahwa .

Terbukti bahwa sin space 54 degree minus sin space 18 degree equals 1 half

Pembahasan

Ingat bahwa: Pembuktian dari ruas kiri: Jadi, Terbukti bahwa .

Ingat bahwa:

Pembuktian dari ruas kiri:

$sin space 54 degree minus sin space 18 degree equals open parentheses sin space 54 degree minus sin space 18 degree close parentheses open parentheses fraction numerator 2 space cos space 18 degree over denominator 2 space cos space 18 degree end fraction close parentheses equals fraction numerator 2 sin space 54 degree space cos space 18 degree minus 2 sin space 18 degree space cos space 18 degree over denominator 2 space cos space 18 degree end fraction equals fraction numerator sin space 72 degree space plus sin space 36 degree minus open parentheses sin space 36 degree plus sin space 0 degree close parentheses over denominator 2 space cos space 18 degree end fraction equals fraction numerator sin space 72 degree space plus sin space 36 degree minus open parentheses sin space 36 degree close parentheses over denominator 2 space cos space 18 degree end fraction equals fraction numerator sin space 72 degree over denominator 2 space cos space 18 degree end fraction equals fraction numerator sin space open parentheses 90 degree minus 18 degree close parentheses over denominator 2 space cos space 18 degree end fraction equals fraction numerator cos space 18 degree over denominator 2 space cos space 18 degree end fraction equals 1 half$

Jadi, Terbukti bahwa sin space 54 degree minus sin space 18 degree equals 1 half .