Pertanyaan

Buktikan identitas trigonometri berikut. sin θ cos θ 1 − 2 cos 2 θ = tan θ − cot θ

Buktikan identitas trigonometri berikut.

$\frac{1 - 2 cos ^{2} θ}{sin θ cos θ} = tan θ - cot θ$

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Klaim

S. Difhayanti

Master Teacher

Mahasiswa/Alumni Universitas Muhammadiyah Prof. Dr. Hamka

Jawaban terverifikasi

Jawaban

terbukti bahwa .

terbukti bahwa $fraction numerator 1 minus 2 space cos squared space theta over denominator sin space theta space cos space theta end fraction equals tan space theta minus cot space theta$ .

Pembahasan

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

Ingat kembali identitas dasar trigonometri berikut.

$table attributes columnalign right center left columnspacing 0px end attributes row cell sin squared space theta plus cos squared space theta end cell equals 1 row cell tan space theta end cell equals cell fraction numerator sin space theta space over denominator cos space theta end fraction end cell row cell cot space theta end cell equals cell fraction numerator cos space theta over denominator sin space theta end fraction end cell end table$

Maka, pembuktian dari identitas trigonometri berikut ini.

$table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator 1 minus 2 space cos squared space theta over denominator sin space theta space cos space theta end fraction end cell equals cell tan space theta minus cot space theta end cell row cell fraction numerator sin squared space theta plus cos squared space theta minus 2 space cos squared space theta over denominator sin space theta space cos space theta end fraction end cell equals cell tan space theta minus cot space theta end cell row cell fraction numerator sin squared space theta minus cos squared space theta over denominator sin space theta space cos space theta end fraction end cell equals cell tan space theta minus cot space theta end cell row cell fraction numerator sin squared space theta over denominator sin space theta space cos space theta end fraction minus fraction numerator cos squared space theta over denominator sin space theta space cos theta end fraction end cell equals cell tan space theta minus cot space theta end cell row cell fraction numerator sin space theta over denominator space cos theta end fraction minus fraction numerator space cos theta over denominator sin space theta end fraction end cell equals cell tan space theta minus cot space theta end cell row cell tan space theta minus cot space theta end cell equals cell tan space theta minus cot space theta space open parentheses Terbukti close parentheses end cell end table$

Jadi, terbukti bahwa $fraction numerator 1 minus 2 space cos squared space theta over denominator sin space theta space cos space theta end fraction equals tan space theta minus cot space theta$ .