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Buktikan identitas trigonometri berikut. h.  1−tan θcos θ​−cot θ−1sin θ​=cos θ+sin θ

Pertanyaan

Buktikan identitas trigonometri berikut.

h.  fraction numerator cos space theta over denominator 1 minus tan space theta end fraction minus fraction numerator sin space theta over denominator cot space theta minus 1 end fraction equals cos space theta plus sin space theta

E. Nur

Master Teacher

Mahasiswa/Alumni Institut Teknologi Sepuluh Nopember

Jawaban terverifikasi

Jawaban

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

Pembahasan

Ingat!

  • tan space theta equals fraction numerator sin space theta over denominator cos space theta end fraction
  • cot space theta equals fraction numerator cos space theta over denominator sin space theta end fraction

Akan dibuktikan

fraction numerator cos space theta over denominator 1 minus tan space theta end fraction minus fraction numerator sin space theta over denominator cot space theta minus 1 end fraction equals cos space theta plus sin space theta

Perhatikan perhitungan berikut

table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator cos space theta over denominator 1 minus tan space theta end fraction minus fraction numerator sin space theta over denominator cot space theta minus 1 end fraction end cell row blank equals cell fraction numerator cos space theta over denominator 1 minus begin display style fraction numerator sin space theta over denominator cos space theta end fraction end style end fraction minus fraction numerator sin space theta over denominator begin display style fraction numerator cos space theta over denominator sin space theta end fraction end style minus 1 end fraction end cell row blank equals cell fraction numerator cos space theta over denominator begin display style fraction numerator cos space theta minus sin theta over denominator cos space theta end fraction end style end fraction minus fraction numerator sin space theta over denominator begin display style fraction numerator cos space theta minus sin space theta over denominator sin space theta end fraction end style end fraction end cell row blank equals cell cos space theta times fraction numerator cos space theta over denominator cos space theta minus sin theta end fraction minus sin space theta times fraction numerator sin space theta over denominator cos space theta minus sin space theta end fraction end cell row blank equals cell fraction numerator cos squared space theta over denominator cos space theta minus sin theta end fraction minus fraction numerator sin squared space theta over denominator cos space theta minus sin theta end fraction end cell row blank equals cell fraction numerator cos squared space theta minus sin squared space theta over denominator cos space theta minus sin theta end fraction end cell row blank equals cell fraction numerator up diagonal strike open parentheses cos space theta minus sin theta close parentheses end strike times open parentheses cos space theta plus sin theta close parentheses over denominator up diagonal strike cos space theta minus sin theta end strike end fraction end cell row blank equals cell cos space theta plus sin theta end cell end table

Dengan demikian terbukti bahwa fraction numerator cos space theta over denominator 1 minus tan space theta end fraction minus fraction numerator sin space theta over denominator cot space theta minus 1 end fraction equals cos space theta plus sin space theta.

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Buktikanlah setiap identitas trigonometri berikut ini. tan A+cot Atan A​=1−cos2A

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