Pertanyaan

Jika secan α − tan α = x untuk 0 ∘ < α < 9 0 ∘ , tentukanlah ( tan α + secan α ) .

Jika  untuk , tentukanlah .

E. Nur

Master Teacher

Mahasiswa/Alumni Institut Teknologi Sepuluh Nopember

Jawaban terverifikasi

Jawaban

hasil dari .

hasil dari table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses tan space alpha plus secan space alpha close parentheses end cell equals cell 1 over x end cell end table.

Pembahasan

Ingat! Diketahui: Perhatikan perhitungan berikut ini! Dengan demikian hasil dari .

Ingat!

  • sin squared alpha plus cos squared alpha equals 1
  • secan space alpha equals fraction numerator 1 over denominator cos space alpha end fraction
  • tan space alpha equals fraction numerator sin space alpha over denominator cos space alpha end fraction

Diketahui:

secan space alpha minus space tan space alpha equals x

Perhatikan perhitungan berikut ini!

table attributes columnalign right center left columnspacing 0px end attributes row cell secan space alpha minus space tan space alpha end cell equals x row cell fraction numerator 1 over denominator cos space alpha end fraction minus fraction numerator sin space alpha over denominator cos space alpha end fraction end cell equals x row cell fraction numerator 1 minus sin space alpha over denominator cos space alpha end fraction end cell equals x row cell fraction numerator 1 minus sin space alpha over denominator cos space alpha end fraction cross times fraction numerator 1 plus sin space alpha over denominator 1 plus sin space alpha end fraction end cell equals x row cell fraction numerator 1 minus sin squared space alpha over denominator cos space alpha open parentheses 1 plus sin space alpha close parentheses end fraction end cell equals x row cell fraction numerator cos squared space alpha over denominator cos space alpha open parentheses 1 plus sin space alpha close parentheses end fraction end cell equals x row cell fraction numerator cos space alpha over denominator open parentheses 1 plus sin space alpha close parentheses end fraction end cell equals x row cell fraction numerator open parentheses 1 plus sin space alpha close parentheses over denominator cos space alpha end fraction end cell equals cell 1 over x end cell row cell fraction numerator 1 over denominator cos space alpha end fraction plus fraction numerator sin space alpha over denominator cos space alpha end fraction end cell equals cell 1 over x end cell row cell secan space alpha plus space tan space alpha end cell equals cell 1 over x end cell row cell tan space alpha plus secan space alpha end cell equals cell 1 over x end cell end table

Dengan demikian hasil dari table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses tan space alpha plus secan space alpha close parentheses end cell equals cell 1 over x end cell end table.

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