Pertanyaan

Buktikan bahwa cos x + cos y sin x − sin y + sin x + sin y cos x − cos y = 0 .

Buktikan bahwa $\frac{sin x - sin y}{cos x + cos y} + \frac{cos x - cos y}{sin x + sin y} = 0$ .

R. Febrianti

Master Teacher

Mahasiswa/Alumni Universitas Negeri Malang

Jawaban terverifikasi

Jawaban

berdasarkan hitungan di atas terbukti bahwa .

berdasarkan hitungan di atas terbukti bahwa $fraction numerator sin space x minus sin space y over denominator cos space x plus cos space y end fraction plus fraction numerator cos space x minus cos space y over denominator sin space x plus sin space y end fraction equals 0$ .

Pembahasan

Diketahui maka berdasarkan sifat perkalian sehinggadiperoleh Berdasarkan identitas trigonometri yaitu maka Jadi berdasarkan hitungan di atas terbukti bahwa .

Diketahui $fraction numerator sin space x minus sin space y over denominator cos space x plus cos space y end fraction plus fraction numerator cos space x minus cos space y over denominator sin space x plus sin space y end fraction$ maka berdasarkan sifat perkalian open parentheses a minus b close parentheses open parentheses a plus b close parentheses equals a squared minus b squared sehingga diperoleh

$begin mathsize 12px style table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator sin space x minus sin space y over denominator cos space x plus cos space y end fraction plus fraction numerator cos space x minus cos space y over denominator open parentheses sin space x plus sin space y close parentheses end fraction end cell equals cell fraction numerator open parentheses sin space x minus sin space y close parentheses open parentheses sin space x plus sin space y close parentheses plus open parentheses cos space x minus cos space y close parentheses open parentheses cos space x plus cos space y close parentheses over denominator open parentheses cos space x plus cos space y close parentheses open parentheses sin space x plus sin space y close parentheses end fraction end cell row blank equals cell fraction numerator sin squared x minus sin squared y plus cos squared x minus cos squared y over denominator open parentheses cos space x plus cos space y close parentheses open parentheses sin space x plus sin space y close parentheses end fraction end cell row blank equals cell fraction numerator sin squared x plus cos squared x minus left parenthesis sin squared y plus cos squared y right parenthesis over denominator open parentheses cos space x plus cos space y close parentheses open parentheses sin space x plus sin space y close parentheses end fraction end cell end table end style$

Berdasarkan identitas trigonometri yaitu sin squared x plus cos squared x equals 1 maka

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

Jadi berdasarkan hitungan di atas terbukti bahwa $fraction numerator sin space x minus sin space y over denominator cos space x plus cos space y end fraction plus fraction numerator cos space x minus cos space y over denominator sin space x plus sin space y end fraction equals 0$ .