Pertanyaan

Sederhanakanlah. a. sin x + cotan x ⋅ cos x

Sederhanakanlah.

a. $sin x + cotan x \cdot cos x$

E. Lestari

Master Teacher

Mahasiswa/Alumni Universitas Sebelas Maret

Jawaban terverifikasi

Jawaban

.

table attributes columnalign right center left columnspacing 0px end attributes row blank blank sin end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank x end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank plus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cotan end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank x end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank times end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cos end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank x end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cosec end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank x end table

Pembahasan

Ingat! Sehingga diperoleh Dengan demikian .

Ingat!

$cotan space x equals fraction numerator cos space x over denominator sin space x end fraction$
$cosec space x equals fraction numerator 1 over denominator sin space x end fraction$

Sehingga diperoleh

$table attributes columnalign right center left columnspacing 0px end attributes row cell sin space x plus cotan space x times cos space x end cell equals cell sin space x plus fraction numerator cos space x over denominator sin space x end fraction times cos space x end cell row blank equals cell sin space x plus fraction numerator cos squared x over denominator sin space x end fraction end cell row blank equals cell fraction numerator sin squared x plus cos squared x over denominator sin x end fraction end cell row blank equals cell fraction numerator 1 over denominator sin space x end fraction end cell row blank equals cell cosec space x end cell end table$

Dengan demikian .