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Pertanyaan

Sederhanakanlah.

d.  cotan space x space open parentheses tan squared x plus 1 close parentheses

E. Lestari

Master Teacher

Mahasiswa/Alumni Universitas Sebelas Maret

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Jawaban

 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 blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open parentheses tan squared x plus 1 close parentheses end cell 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 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 times end table 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.

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 squared x plus 1 equals sec squared x

Sehingga diperoleh

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

Dengan demikian 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 blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open parentheses tan squared x plus 1 close parentheses end cell 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 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 times end table 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.

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Pertanyaan serupa

Tunjukkan kebenaran identitas trigonometri berikut. g.  (secanB−cosecB)(sinB+cosB)=tanB⋅cotanB

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