Pertanyaan

Buktikan identitas berikut ini. b. cos θ 1 − sin θ + 1 − sin θ cos θ = 2 sec θ

Buktikan identitas berikut ini.

b. $\frac{1 - sin θ}{cos θ} + \frac{cos θ}{1 - sin θ} = 2 sec θ$

F. Kartikasari

Master Teacher

Mahasiswa/Alumni Universitas Negeri Surabaya

Jawaban terverifikasi

Jawaban

terbukti bahwa .

terbukti bahwa $begin mathsize 14px style fraction numerator 1 minus sin space theta over denominator cos space theta end fraction plus fraction numerator cos space theta over denominator 1 minus sin space theta end fraction equals 2 space sec space theta end style$ .

Pembahasan

Jadi, terbukti bahwa .

$begin mathsize 11px style table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator 1 minus sin space theta over denominator cos space theta end fraction plus fraction numerator cos space theta over denominator 1 minus sin space theta end fraction end cell equals cell fraction numerator open parentheses 1 minus sin space theta close parentheses open parentheses 1 minus sin space theta close parentheses plus open parentheses cos space theta close parentheses open parentheses cos space theta close parentheses over denominator open parentheses cos space theta close parentheses open parentheses 1 minus sin space theta close parentheses end fraction end cell row blank equals cell fraction numerator 1 minus 2 space sin space theta plus sin squared theta plus cos squared theta over denominator cos space theta minus sin space theta space cos space theta end fraction end cell row blank equals cell fraction numerator 1 minus 2 space sin space theta plus 1 over denominator cos space theta open parentheses 1 minus sin space theta close parentheses end fraction end cell row blank equals cell fraction numerator 2 open parentheses 1 minus sin space theta close parentheses over denominator cos space theta open parentheses 1 minus sin space theta close parentheses end fraction end cell row blank equals cell fraction numerator 2 over denominator cos space theta end fraction end cell row blank equals cell 2 space sec space theta end cell end table end style$

Jadi, terbukti bahwa $begin mathsize 14px style fraction numerator 1 minus sin space theta over denominator cos space theta end fraction plus fraction numerator cos space theta over denominator 1 minus sin space theta end fraction equals 2 space sec space theta end style$ .