3. Buktikanlah identitas-identitas trigonometri berikut. d. cos x(1+tan2 x)=secan x

Pertanyaan

3. Buktikanlah identitas-identitas trigonometri berikut.

d. cos space x open parentheses 1 plus tan squared space x close parentheses equals secan space x 

P. Tessalonika

Master Teacher

Mahasiswa/Alumni Universitas Negeri Medan

Jawaban terverifikasi

Jawaban

terbukti bahwa cos space x open parentheses 1 plus tan squared space x close parentheses equals secan space x.

Pembahasan

Untuk membuktikan persamaan tersebut, kita akan menyederhanakan ruas kiri untuk mendapatkan persamaan di ruas kanan, kemudian ingat kembali identitas trigonometri berikut.

  • tan space x equals fraction numerator sin space x over denominator cos space x end fraction left right double arrow tan squared space x equals fraction numerator sin squared space x over denominator cos to the power of 2 space end exponent x end fraction 
  • sin squared space x plus cos squared space x equals 1 
  • secan space x equals fraction numerator 1 over denominator cos space x end fraction 

Sehingga diperoleh:

table attributes columnalign right center left columnspacing 0px end attributes row cell cos space x open parentheses 1 plus tan squared space x close parentheses end cell equals cell secan space x end cell row cell cos space x open parentheses 1 plus fraction numerator sin squared space x over denominator cos squared space x end fraction close parentheses end cell equals cell secan space x end cell row cell cos space x open parentheses fraction numerator cos squared space x over denominator cos squared space x end fraction plus fraction numerator sin squared space x over denominator cos squared space x end fraction close parentheses end cell equals cell secan space x end cell row cell up diagonal strike cos space x end strike open parentheses fraction numerator sin squared space x plus cos squared space x over denominator cos to the power of up diagonal strike 2 end exponent space x end fraction close parentheses end cell equals cell secan space x end cell row cell fraction numerator 1 over denominator cos space x end fraction end cell equals cell secan space x end cell row cell secan space x end cell equals cell secan space x space begin bold style left parenthesis terbukti right parenthesis end style end cell row blank blank blank end table 

Dengan demikian, terbukti bahwa cos space x open parentheses 1 plus tan squared space x close parentheses equals secan space x.

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