Pertanyaan

Buktikan identitas trigonometri berikut. sin θ + cos θ sin 3 θ + cos 3 θ = 1 − sin θ cos θ

Buktikan identitas trigonometri berikut.

$\frac{sin ^{3} θ + cos ^{3} θ}{sin θ + cos θ} = 1 - sin θ cos θ$

A. Salim

Master Teacher

Mahasiswa/Alumni Universitas Pelita Harapan

Jawaban terverifikasi

Jawaban

terbukti bahwa .

terbukti bahwa $fraction numerator sin cubed space theta plus cos cubed space theta over denominator sin space theta plus cos space theta end fraction equals 1 minus sin space theta space cos space theta$ .

Pembahasan

Ingat kembali identitas dasar trigonometri berikut. Maka, pembuktian dari identitas trigonometri berikut ini. Jadi, terbukti bahwa .

Ingat kembali identitas dasar trigonometri berikut.

sin squared space ϑ plus cos squared space theta equals 1

Maka, pembuktian dari identitas trigonometri berikut ini.

$table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator sin cubed space theta plus cos cubed space theta over denominator sin space theta plus cos space theta end fraction end cell equals cell 1 minus sin space theta space cos space theta end cell row cell fraction numerator open parentheses up diagonal strike sin space theta plus cos space theta end strike close parentheses open parentheses sin space theta squared minus sin space theta times cos space theta plus cos space theta squared close parentheses over denominator up diagonal strike sin space theta plus cos space theta end strike end fraction end cell equals cell 1 minus sin space theta space cos space theta end cell row cell sin space theta squared minus sin space theta space cos space theta plus cos space theta squared end cell equals cell 1 minus sin space theta space cos space theta end cell row cell 1 minus sin space theta space cos space theta end cell equals cell 1 minus sin space theta space cos space theta space open parentheses Terbukti close parentheses end cell end table$

Jadi, terbukti bahwa $fraction numerator sin cubed space theta plus cos cubed space theta over denominator sin space theta plus cos space theta end fraction equals 1 minus sin space theta space cos space theta$ .