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Buktikan identitas trigonometri berikut. g.  tan θ+cot θsec θ+csc θ​=sin θ+cos θ

Pertanyaan

Buktikan identitas trigonometri berikut.

g.  fraction numerator sec space theta plus csc space theta over denominator tan space theta plus cot space theta end fraction equals sin space theta plus cos space theta

E. Nur

Master Teacher

Mahasiswa/Alumni Institut Teknologi Sepuluh Nopember

Jawaban terverifikasi

Jawaban

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

Pembahasan

Ingat!

  • sec space theta equals fraction numerator 1 over denominator cos space theta end fraction
  • csc space theta equals fraction numerator 1 over denominator sin space theta end fraction
  • 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
  • sin space squared theta plus cos squared space theta equals 1

Akan dibuktikan

fraction numerator sec space theta plus csc space theta over denominator tan space theta plus cot space theta end fraction equals sin space theta plus cos space theta

Perhatikan perhitungan berikut

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

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

27

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