Pertanyaan

Buktikan identitas trigonometri berikut. cos 2 x sin 2 x − sin 2 x cos 2 x = sec 2 x − cosec 2 x

Buktikan identitas trigonometri berikut.

$\frac{sin ^{2} x}{cos ^{2} x} - \frac{cos ^{2} x}{sin ^{2} x} = sec^{2} x - cosec^{2} x$

K. Putri

Master Teacher

Mahasiswa/Alumni Universitas Pendidikan Ganesha

Jawaban terverifikasi

Pembahasan

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator sin squared space straight x over denominator cos squared space straight x end fraction minus fraction numerator cos squared space straight x over denominator sin squared space straight x end fraction end cell equals cell fraction numerator sin squared space straight x open parentheses sin squared space straight x close parentheses over denominator cos squared space straight x open parentheses sin squared space straight x close parentheses end fraction minus fraction numerator cos squared space straight x open parentheses cos squared space straight x close parentheses over denominator sin squared space straight x open parentheses cos squared space straight x close parentheses end fraction end cell row blank equals cell fraction numerator sin to the power of 4 space straight x minus cos to the power of 4 space straight x over denominator cos squared space straight x space sin squared space straight x end fraction end cell row blank equals cell fraction numerator open parentheses sin squared space straight x minus cos squared space straight x close parentheses open parentheses sin squared space straight x plus cos squared space straight x close parentheses over denominator cos squared space straight x space sin squared space straight x end fraction end cell row blank equals cell fraction numerator open parentheses sin squared space straight x minus cos squared space straight x close parentheses over denominator cos squared space straight x space sin squared space straight x end fraction end cell row blank equals cell fraction numerator 1 over denominator cos squared space straight x end fraction minus fraction numerator 1 over denominator sin squared space straight x end fraction end cell row blank equals cell sec squared space straight x minus cosec squared space straight x end cell end table end style$