Pertanyaan

Buktikan: cotan x cotan x − cos x = 1 + sin x cos 2 x

Buktikan:

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

R. RGFLLIMA

Master Teacher

Jawaban terverifikasi

Jawaban

i, terbukti

i, terbukti $fraction numerator cotan space straight x minus cos space straight x over denominator cotan space straight x end fraction equals fraction numerator cos squared straight x over denominator 1 plus sin space straight x end fraction$

Pembahasan

Identitas trigonometeri. Pembuktian: Jadii, terbukti

Identitas trigonometeri.

Pembuktian: $fraction numerator cotan space straight x minus cos space straight x over denominator cotan space straight x end fraction equals fraction numerator cos squared straight x over denominator 1 plus sin space straight x end fraction$

$table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator cotan space straight x minus cos space straight x over denominator cotan space straight x end fraction end cell equals cell fraction numerator cotan space straight x over denominator cotan space straight x end fraction minus fraction numerator cos space straight x over denominator cotan space straight x end fraction end cell row blank equals cell 1 minus fraction numerator cos space straight x over denominator begin display style fraction numerator 1 over denominator tan space straight x end fraction end style end fraction end cell row blank equals cell 1 minus cos space straight x times tan space straight x end cell row blank equals cell 1 minus sin space straight x end cell row blank equals cell fraction numerator left parenthesis 1 minus sin space straight x right parenthesis left parenthesis 1 plus sin space straight x right parenthesis over denominator 1 plus sin space straight x end fraction end cell row blank equals cell fraction numerator 1 minus sin squared straight x over denominator 1 plus sin space straight x end fraction end cell row blank equals cell fraction numerator cos squared space straight x over denominator 1 plus sin space straight x end fraction end cell end table$

Jadii, terbukti $fraction numerator cotan space straight x minus cos space straight x over denominator cotan space straight x end fraction equals fraction numerator cos squared straight x over denominator 1 plus sin space straight x end fraction$