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Pertanyaan

Sederhanakanlah.

j.  secan space x times cosec space x minus cotan space x

E. Lestari

Master Teacher

Mahasiswa/Alumni Universitas Sebelas Maret

Jawaban terverifikasi

Jawaban

 table attributes columnalign right center left columnspacing 0px end attributes row blank blank secan end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank x end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank times end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cosec end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank x end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cotan end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank x end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank tan end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank x end table.

Pembahasan

Ingat!

  • cosec space x equals fraction numerator 1 over denominator sin space x end fraction
  • secan space x equals fraction numerator 1 over denominator cos space x end fraction
  • tan space x equals fraction numerator sin space x over denominator cos space x end fraction
  • cotan space x equals fraction numerator cos space x over denominator sin space x end fraction
  • sin squared x plus cos squared x equals 1

Sehingga diperoleh

table attributes columnalign right center left columnspacing 0px end attributes row cell secan space x times cosec space x minus cotan space x end cell equals cell fraction numerator 1 over denominator cos space x end fraction times fraction numerator 1 over denominator sin space x end fraction minus fraction numerator cos space x over denominator sin space x end fraction end cell row blank equals cell fraction numerator 1 over denominator sin space x space cos space x end fraction minus fraction numerator cos space x over denominator sin space x end fraction end cell row blank equals cell fraction numerator 1 over denominator sin space x space cos space x end fraction minus fraction numerator cos squared x over denominator sin space x space cos space x end fraction end cell row blank equals cell fraction numerator 1 minus cos squared x over denominator sin space x space cos space x end fraction end cell row blank equals cell fraction numerator sin squared x over denominator sin space x space cos space x end fraction end cell row blank equals cell fraction numerator up diagonal strike sin space x end strike times sin space x over denominator up diagonal strike sin space x end strike times cos space x end fraction end cell row blank equals cell fraction numerator sin space x over denominator cos space x end fraction end cell row blank equals cell tan space x end cell end table

Dengan demikian table attributes columnalign right center left columnspacing 0px end attributes row blank blank secan end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank x end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank times end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cosec end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank x end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cotan end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank x end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank tan end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank x end table.

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