Pertanyaan

Buktikan identitas trigonometri berikut. sin x 1 − cos x + 1 − cos x sin x = 2 cos ec x

Buktikan identitas trigonometri berikut.

$\frac{1 - cos x}{sin x} + \frac{sin x}{1 - cos x} = 2 cos ec x$

K. Putri

Master Teacher

Mahasiswa/Alumni Universitas Pendidikan Ganesha

Jawaban terverifikasi

Pembahasan

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