Pertanyaan

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

Buktikan identitas trigonometri berikut.

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

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Klaim

S. Difhayanti

Master Teacher

Mahasiswa/Alumni Universitas Muhammadiyah Prof. Dr. Hamka

Jawaban terverifikasi

Jawaban

terbukti bahwa .

terbukti bahwa $fraction numerator sin space theta space cos space over denominator cos squared space theta minus sin to the power of 2 space end exponent theta end fraction equals fraction numerator tan space theta over denominator 1 minus tan squared space theta end fraction$ .

Pembahasan

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

Ingat kembali identitas dasar trigonometri berikut.

$tan space theta equals fraction numerator sin space theta over denominator cos space theta end fraction$

Maka, pembuktian dari identitas trigonometri berikut ini.

$table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator sin space theta space cos space over denominator cos squared space theta minus sin to the power of 2 space end exponent theta end fraction end cell equals cell fraction numerator tan space theta over denominator 1 minus tan squared space theta end fraction end cell row cell fraction numerator sin space theta space cos space over denominator cos squared space theta minus sin to the power of 2 space end exponent theta end fraction end cell equals cell fraction numerator begin display style fraction numerator sin space theta over denominator cos space theta end fraction end style over denominator 1 minus open parentheses begin display style fraction numerator sin space theta over denominator cos space space theta end fraction end style close parentheses squared end fraction end cell row cell fraction numerator sin space theta space cos space over denominator cos squared space theta minus sin to the power of 2 space end exponent theta end fraction end cell equals cell fraction numerator begin display style fraction numerator sin space theta over denominator cos space theta end fraction end style over denominator 1 minus begin display style fraction numerator sin space theta squared over denominator cos space space theta squared end fraction end style end fraction end cell row cell fraction numerator sin space theta space cos space over denominator cos squared space theta minus sin to the power of 2 space end exponent theta end fraction end cell equals cell fraction numerator begin display style fraction numerator begin display style fraction numerator sin space theta over denominator cos space theta end fraction end style over denominator cos space space theta squared minus sin space theta squared end fraction end style over denominator cos space theta squared end fraction end cell row cell fraction numerator sin space theta space cos space over denominator cos squared space theta minus sin to the power of 2 space end exponent theta end fraction end cell equals cell fraction numerator begin display style sin space theta space cos theta end style over denominator cos space theta squared minus sin space theta squared end fraction space open parentheses Terbukti close parentheses end cell end table$

Jadi, terbukti bahwa $fraction numerator sin space theta space cos space over denominator cos squared space theta minus sin to the power of 2 space end exponent theta end fraction equals fraction numerator tan space theta over denominator 1 minus tan squared space theta end fraction$ .