Pertanyaan

Buktikan bahwa: 3 − 5 cos x 5 cos x − 4 − 4 + 5 cos x 3 + 5 sin x = 0

Buktikan bahwa: $\frac{5 cos x - 4}{3 - 5 cos x} - \frac{3 + 5 sin x}{4 + 5 cos x} = 0$

Y. Fathoni

Master Teacher

Mahasiswa/Alumni Universitas Negeri Yogyakarta.

Jawaban terverifikasi

Jawaban

terbukti bahwa .

terbukti bahwa $fraction numerator 5 space cos space x minus 4 over denominator 3 minus 5 space cos space x end fraction minus fraction numerator 3 plus sin space x over denominator 4 plus 5 space cos space x end fraction equals 0$ .

Pembahasan

Ingat kembali konsep identitas trigonometri berikut. Soal tersebut tidak dapat terbukti karena terdapat kesalahan, soal yang benar yaitu . Perhatikan perhitungan berikut. Dengan demikian terbukti bahwa .

Ingat kembali konsep identitas trigonometri berikut.

sin squared space x plus cos squared space x equals 1

Soal tersebut tidak dapat terbukti karena terdapat kesalahan, soal yang benar yaitu $fraction numerator 5 space cos space x minus 4 over denominator 3 minus 5 space sin space x end fraction minus fraction numerator 3 plus 5 space sin space x over denominator 4 plus 5 space cos space x end fraction equals 0$ .

Perhatikan perhitungan berikut.

$table attributes columnalign right center left columnspacing 2px end attributes row blank blank cell fraction numerator 5 space cos space x minus 4 over denominator 3 minus 5 space sin space x end fraction minus fraction numerator 3 plus 5 space sin space x over denominator 4 plus 5 space cos space x end fraction end cell row blank equals cell fraction numerator open parentheses 5 space cos space x minus 4 close parentheses open parentheses 4 plus 5 space cos space x close parentheses minus open parentheses 3 plus 5 space sin space x close parentheses open parentheses 3 minus 5 space sin space x close parentheses over denominator open parentheses 3 minus 5 space sin space x close parentheses open parentheses 4 plus 5 space cos space x close parentheses end fraction end cell row blank equals cell fraction numerator open parentheses 5 space cos space x minus 4 close parentheses open parentheses 5 space cos space x plus 4 close parentheses minus open parentheses 3 plus 5 space sin space x close parentheses open parentheses 3 minus 5 space sin space x close parentheses over denominator open parentheses 3 minus 5 space sin space x close parentheses open parentheses 4 plus 5 space cos space x close parentheses end fraction end cell row blank equals cell fraction numerator open square brackets open parentheses 5 space cos space x close parentheses squared minus open parentheses 4 close parentheses squared close square brackets minus open square brackets open parentheses 3 close parentheses squared minus open parentheses 5 space sin space x close parentheses squared close square brackets over denominator 12 plus 15 space cos space x minus 20 space sin space x minus 25 space sin space x space cos space x end fraction end cell row blank equals cell fraction numerator open parentheses 25 space cos squared space x minus 16 close parentheses minus open parentheses 9 minus 25 space sin squared space x close parentheses over denominator 12 plus 15 space cos space x minus 20 space sin space x minus 25 space sin space x space cos space x end fraction end cell row blank equals cell fraction numerator 25 space cos squared space x minus 16 minus 9 plus 25 space sin squared space x over denominator 12 plus 15 space cos space x minus 20 space sin space x minus 25 space sin space x space cos space x end fraction end cell row blank equals cell fraction numerator 25 open parentheses sin squared space x plus cos squared space x close parentheses minus 25 over denominator 12 plus 15 space cos space x minus 20 space sin space x minus 25 space sin space x space cos space x end fraction end cell row blank equals cell fraction numerator 25 times 1 minus 25 over denominator 12 plus 15 space cos space x minus 20 space sin space x minus 25 space sin space x space cos space x end fraction end cell row blank equals cell fraction numerator 25 minus 25 over denominator 12 plus 15 space cos space x minus 20 space sin space x minus 25 space sin space x space cos space x end fraction end cell row blank equals cell fraction numerator 0 over denominator 12 plus 15 space cos space x minus 20 space sin space x minus 25 space sin space x space cos space x end fraction end cell row blank equals 0 end table$

Dengan demikian terbukti bahwa $fraction numerator 5 space cos space x minus 4 over denominator 3 minus 5 space cos space x end fraction minus fraction numerator 3 plus sin space x over denominator 4 plus 5 space cos space x end fraction equals 0$ .