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Buktikan identitas trigonometri berikut. sin x−cos x(1−cotan2 x) sin x​=1+cotan x

Pertanyaan

Buktikan identitas trigonometri berikut.

begin mathsize 14px style fraction numerator left parenthesis 1 minus cotan squared space straight x right parenthesis space sin space straight x over denominator sin space straight x minus cos space straight x end fraction equals 1 plus cotan space straight x end style  

  1. begin mathsize 14px style.... end style  

  2. undefined 

N. Mustikowati

Master Teacher

Mahasiswa/Alumni Universitas Negeri Jakarta

Jawaban terverifikasi

Pembahasan

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator open parentheses 1 minus cotan squared space straight x close parentheses space sin space straight x over denominator sin space straight x minus cos space straight x end fraction end cell equals cell fraction numerator open parentheses 1 minus begin display style fraction numerator cos squared space straight x over denominator sin squared space straight x end fraction end style close parentheses sin space straight x over denominator sin space straight x minus cos space straight x end fraction end cell row blank equals cell fraction numerator open parentheses begin display style fraction numerator sin squared space straight x minus cos squared space straight x over denominator sin squared space straight x end fraction end style close parentheses sin space straight x over denominator sin space straight x minus cos space straight x end fraction end cell row blank equals cell fraction numerator open parentheses begin display style fraction numerator sin squared space straight x minus cos squared space straight x over denominator sin space straight x end fraction end style close parentheses over denominator sin space straight x minus cos space straight x end fraction end cell row blank equals cell fraction numerator open parentheses sin space straight x minus cos space straight x close parentheses open parentheses sin space straight x plus cos space straight x close parentheses over denominator open parentheses sin space straight x minus cos space straight x close parentheses space sin space straight x end fraction end cell row blank equals cell fraction numerator sin space straight x plus cos space straight x over denominator sin space straight x end fraction end cell row blank equals cell fraction numerator sin space straight x over denominator sin space straight x end fraction plus fraction numerator cos space straight x over denominator sin space straight x end fraction end cell row blank equals cell 1 plus cotan space straight x end cell end table end style 

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Pertanyaan serupa

Buktikanlah setiap identitas trigonometri berikut ini: 1) (cosx+sinx)(cosx−sinx)=1−2sin2x

222

4.7

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