Pertanyaan

Buktikan identitas trigonometri berikut. sin x − cos x ( 1 − cotan 2 x ) sin x = 1 + cotan x

Buktikan identitas trigonometri berikut.

$\frac{( 1 - cotan ^{2} x ) sin x}{sin x - cos x} = 1 + cotan x$

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$