Pertanyaan

Buktikan identitas trigonometri berikut. 1 − sin x 1 − 1 + sin x 1 = 2 tan x sec x

Buktikan identitas trigonometri berikut.

$\frac{1}{1 - sin x} - \frac{1}{1 + sin x} = 2 tan x sec x$

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Habis dalam

Klaim

K. Putri

Master Teacher

Mahasiswa/Alumni Universitas Pendidikan Ganesha

Jawaban terverifikasi

Pembahasan

$begin mathsize 14px style fraction numerator 1 over denominator 1 minus sin space x end fraction minus fraction numerator 1 over denominator 1 plus sin space x end fraction equals fraction numerator open parentheses 1 plus sin space x close parentheses over denominator open parentheses 1 minus sin space x close parentheses open parentheses 1 plus sin space x close parentheses end fraction minus fraction numerator open parentheses 1 minus sin space x close parentheses over denominator open parentheses 1 minus sin space x close parentheses open parentheses 1 plus sin space x close parentheses end fraction equals fraction numerator 1 plus sin space x minus 1 plus sin space x over denominator 1 minus sin squared space x end fraction equals fraction numerator 2 space sin space x over denominator cos squared space x end fraction equals 2 times fraction numerator sin space x over denominator cos space x end fraction times fraction numerator 1 over denominator cos space x end fraction equals 2 space tan space x space s e c space x end style$