Buktikan identitas-identitas trigonometri berikut: (sin α cot α)21=sec2 α

Pertanyaan

Buktikan identitas-identitas trigonometri berikut:

$\frac1{\left(\sin\;\alpha\;\cot\;\alpha\right)^2}=\sec^2\;\alpha$

H. Endah

Master Teacher

Mahasiswa/Alumni Universitas Negeri Yogyakarta

Jawaban terverifikasi

Jawaban

terbukti bahwa 1 over open parentheses sin space alpha space cot space alpha close parentheses squared equals sec squared space alpha

Pembahasan

Pembuktian dari ruas kiri didapatkan:

$table attributes columnalign right center left columnspacing 0px end attributes row cell 1 over open parentheses sin space alpha space cot space alpha close parentheses squared end cell equals cell fraction numerator 1 over denominator sin squared space alpha space cot squared space alpha space end fraction end cell row blank equals cell fraction numerator 1 over denominator down diagonal strike sin squared space alpha end strike space times begin display style fraction numerator cos squared space alpha over denominator down diagonal strike sin squared space alpha space end strike end fraction end style end fraction end cell row blank equals cell fraction numerator 1 over denominator cos squared space alpha end fraction end cell row blank equals cell sec squared space alpha end cell end table$

Jadi, terbukti bahwa 1 over open parentheses sin space alpha space cot space alpha close parentheses squared equals sec squared space alpha .