Pertanyaan

Buktikanlah setiap identitas trigonometri berikut ini. 1 − tan β cos β + 1 − co tβ sin β = sin β + cos β

Buktikanlah setiap identitas trigonometri berikut ini.

$\frac{cos β}{1 - tan β} + \frac{sin β}{1 - co tβ} = sin β + cos β$

D. Kamilia

Master Teacher

Mahasiswa/Alumni Universitas Negeri Malang

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Terbukti.

$begin mathsize 14px style table attributes columnalign right center left columnspacing 2px end attributes row cell fraction numerator cos space beta over denominator 1 minus tan space beta end fraction plus fraction numerator sin space beta over denominator 1 minus cot space beta end fraction end cell equals cell sin space beta plus cos beta end cell row cell fraction numerator cos space beta over denominator 1 minus begin display style fraction numerator sin space beta over denominator cos space beta end fraction end style end fraction plus fraction numerator sin space beta over denominator 1 minus begin display style fraction numerator cos space beta over denominator sin space beta end fraction end style end fraction end cell equals cell sin space beta plus cos space beta end cell row cell fraction numerator cos space beta over denominator begin display style fraction numerator cos space beta minus sin space beta over denominator cos space beta end fraction end style end fraction plus fraction numerator sin space beta over denominator begin display style fraction numerator sin space beta minus cos space beta over denominator sin space beta end fraction end style end fraction end cell equals cell sin space beta plus cos space beta end cell row cell negative fraction numerator cos squared space beta over denominator begin display style sin space beta minus cos space beta end style end fraction plus fraction numerator sin squared space beta over denominator begin display style sin space beta minus cos space beta end style end fraction end cell equals cell sin space beta plus cos space beta end cell row cell fraction numerator sin squared space beta minus cos squared space beta over denominator begin display style sin space beta minus cos space beta end style end fraction end cell equals cell sin space beta plus cos space beta end cell row cell fraction numerator open parentheses sin space beta minus cos space beta close parentheses open parentheses sin space beta plus cos space beta close parentheses over denominator begin display style sin space beta minus cos space beta end style end fraction end cell equals cell sin space beta plus cos space beta end cell row cell sin space beta plus cos space beta end cell equals cell sin space beta plus cos space beta end cell end table end style$

Terbukti.