Buktikan bahwa cos x1+sin x+1+sin xcos x=cos x2 dan cari semua besar sudut antara −180∘ dan 180∘ yang merupakan solusi dari persamaan (1+sinx)2+cos2x=4cos x (1+sin x).

Pertanyaan

Buktikan bahwa $fraction numerator 1 plus sin space x over denominator cos space x end fraction plus fraction numerator cos space x over denominator 1 plus sin space x end fraction equals fraction numerator 2 over denominator cos space x end fraction$ dan cari semua besar sudut antara $-180^\circ$ dan $180^\circ$ yang merupakan solusi dari persamaan $\left(1+\sin x\right)^2+\cos^2x=4\cos\;x\;(1+\sin\;x)$ .

I. Sutiawan

Master Teacher

Mahasiswa/Alumni Universitas Pasundan

Jawaban terverifikasi

Jawaban

himpunan penyelesaian dari persamaan trigonometri tersebut adalah open curly brackets negative 60 degree comma space minus 90 degree comma space 60 degree close curly brackets

open curly brackets negative 60 degree comma space minus 90 degree comma space 60 degree close curly brackets

Pembahasan

$begin mathsize 12px style table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator 1 plus sin space x over denominator cos space x end fraction plus fraction numerator cos space x over denominator 1 plus sin space x end fraction end cell equals cell fraction numerator 1 plus sin space x over denominator cos space x end fraction plus fraction numerator cos space x over denominator 1 plus sin space x end fraction cross times fraction numerator 1 minus sin space x over denominator 1 minus sin space x end fraction end cell row blank equals cell fraction numerator 1 plus sin space x over denominator cos space x end fraction plus fraction numerator cos space x space left parenthesis 1 minus sin space x right parenthesis over denominator 1 minus sin squared x end fraction end cell row blank equals cell fraction numerator 1 plus sin space x over denominator cos space x end fraction plus fraction numerator cos space x space left parenthesis 1 minus sin space x right parenthesis over denominator cos squared x end fraction end cell row blank equals cell fraction numerator 1 plus sin space x over denominator cos space x end fraction plus fraction numerator 1 minus sin space x over denominator cos space x end fraction end cell row blank equals cell fraction numerator 1 plus sin space x plus 1 minus sin space x over denominator cos space x end fraction end cell row blank equals cell fraction numerator 2 over denominator cos space x end fraction space left parenthesis terbukti right parenthesis end cell end table end style$

begin mathsize 12px style open parentheses 1 plus sin x close parentheses squared plus cos squared x equals 4 cos space x space left parenthesis 1 plus sin space x right parenthesis end style

begin mathsize 12px style sin space x equals negative 1 space atau space cos space x equals 1 half end style

Jadi, himpunan penyelesaian dari persamaan trigonometri tersebut adalah .