Pertanyaan

Buktikan identitas trigonometri berikut. c. tan θ − 1 1 + tan θ − sin θ − cos θ 2 cos θ = 1

Buktikan identitas trigonometri berikut.

c. $\frac{1 + tan θ}{tan θ - 1} - \frac{2 cos θ}{sin θ - cos θ} = 1$

E. Nur

Master Teacher

Mahasiswa/Alumni Institut Teknologi Sepuluh Nopember

Jawaban terverifikasi

Jawaban

terbukti bahwa .

terbukti bahwa $fraction numerator 1 plus tan space theta over denominator tan space theta minus 1 end fraction minus fraction numerator 2 space cos space theta over denominator sin space theta minus cos space theta end fraction equals 1$ .

Pembahasan

Ingat! Akan dibuktikan Perhatikan perhitungan berikut Dengan demikian terbukti bahwa .

Ingat!

$tan space theta equals fraction numerator sin space theta over denominator cos space theta end fraction$

Akan dibuktikan

$fraction numerator 1 plus tan space theta over denominator tan space theta minus 1 end fraction minus fraction numerator 2 space cos space theta over denominator sin space theta minus cos space theta end fraction equals 1$

Perhatikan perhitungan berikut

$table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator 1 plus space tan space theta over denominator tan space theta minus 1 end fraction minus fraction numerator 2 space cos space theta over denominator sin space theta minus cos space theta end fraction end cell row blank equals cell fraction numerator 1 plus begin display style fraction numerator sin space theta over denominator cos space theta end fraction end style over denominator begin display style fraction numerator sin space theta over denominator cos space theta end fraction minus 1 end style end fraction minus fraction numerator 2 space cos space theta over denominator sin space theta minus cos space theta end fraction end cell row blank equals cell fraction numerator begin display style fraction numerator cos space theta plus sin space theta over denominator up diagonal strike cos space theta end strike end fraction end style over denominator begin display style fraction numerator sin space theta minus cos space theta over denominator up diagonal strike cos space theta end strike end fraction end style end fraction minus fraction numerator 2 space cos space theta over denominator sin space theta minus cos space theta end fraction end cell row blank equals cell fraction numerator cos space theta plus sin space theta over denominator sin space theta minus cos space theta end fraction minus fraction numerator 2 space cos space theta over denominator sin space theta minus cos space theta end fraction end cell row blank equals cell fraction numerator cos space theta plus sin space theta minus 2 space cos space theta over denominator sin space theta minus cos space theta end fraction end cell row blank equals cell fraction numerator sin space theta minus cos space theta over denominator sin space theta minus cos space theta end fraction end cell row blank equals 1 end table$

Dengan demikian terbukti bahwa $fraction numerator 1 plus tan space theta over denominator tan space theta minus 1 end fraction minus fraction numerator 2 space cos space theta over denominator sin space theta minus cos space theta end fraction equals 1$ .