Pertanyaan

Buktikan identitas trigonometri berikut. i. tan θ sec θ − sin θ = sin 3 θ sec 2 θ

Buktikan identitas trigonometri berikut.

i. $tan θ sec θ - sin θ = sin^{3} θ sec^{2} θ$

E. Nur

Master Teacher

Mahasiswa/Alumni Institut Teknologi Sepuluh Nopember

Jawaban terverifikasi

Jawaban

terbukti bahwa .

terbukti bahwa tan space theta space sec space theta minus sin space theta equals sin cubed space theta space sec squared space theta

Pembahasan

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

Ingat!

$tan space theta equals fraction numerator sin space theta over denominator cos space theta end fraction$
$sec space theta equals fraction numerator 1 over denominator cos space theta end fraction$

Akan dibuktikan

tan space theta space sec space theta minus sin space theta equals sin cubed space theta space sec squared space theta

Perhatikan perhitungan berikut

$table attributes columnalign right center left columnspacing 0px end attributes row cell tan space theta space sec space theta minus sin space theta end cell equals cell fraction numerator sin space theta over denominator cos space theta end fraction times fraction numerator 1 over denominator cos space theta end fraction minus sin space theta end cell row blank equals cell fraction numerator sin space theta over denominator cos squared theta end fraction minus sin space theta end cell row blank equals cell fraction numerator sin space theta minus sin space theta times cos squared theta over denominator cos squared theta end fraction end cell row blank equals cell fraction numerator sin space theta open parentheses 1 minus cos squared theta close parentheses over denominator cos squared theta end fraction end cell row blank equals cell fraction numerator sin space theta times sin squared theta over denominator cos squared theta end fraction end cell row blank equals cell fraction numerator sin cubed theta over denominator cos squared theta end fraction end cell row blank equals cell sin cubed theta times fraction numerator 1 over denominator cos squared theta end fraction end cell row blank equals cell sin cubed theta times sec squared theta end cell end table$

Dengan demikian terbukti bahwa tan space theta space sec space theta minus sin space theta equals sin cubed space theta space sec squared space theta .