Pertanyaan

Buktikan identitas trigonometri berikut. f. 1 − sin α cos 2 α − 1 + sin α cos 2 α = 2 sin α

Buktikan identitas trigonometri berikut.

f. $\frac{cos ^{2} α}{1 - sin α} - \frac{cos ^{2} α}{1 + sin α} = 2 sin α$

E. Nur

Master Teacher

Mahasiswa/Alumni Institut Teknologi Sepuluh Nopember

Jawaban terverifikasi

Jawaban

terbukti bahwa .

terbukti bahwa $fraction numerator cos squared alpha over denominator 1 minus sin space alpha end fraction minus fraction numerator cos squared alpha over denominator 1 plus sin space alpha end fraction equals 2 space sin space alpha$ .

Pembahasan

Ingat! sehingga . Akan dibuktikan Perhatikan perhitungan berikut. Dengan demikian terbukti bahwa .

Ingat!

sehingga .

Akan dibuktikan

$fraction numerator cos squared alpha over denominator 1 minus sin space alpha end fraction minus fraction numerator cos squared alpha over denominator 1 plus sin space alpha end fraction equals 2 space sin space alpha$

Perhatikan perhitungan berikut.

$table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator cos squared alpha over denominator 1 minus sin space alpha end fraction minus fraction numerator cos squared alpha over denominator 1 plus sin space alpha end fraction end cell equals cell cos squared alpha open parentheses fraction numerator 1 over denominator 1 minus sin space alpha end fraction minus fraction numerator 1 over denominator 1 plus sin space alpha end fraction close parentheses end cell row blank equals cell cos squared alpha open parentheses fraction numerator open parentheses 1 plus sin space alpha close parentheses minus open parentheses 1 minus sin space alpha close parentheses over denominator open parentheses 1 minus sin space alpha close parentheses open parentheses 1 plus sin space alpha close parentheses end fraction close parentheses end cell row blank equals cell cos squared alpha open parentheses fraction numerator 1 plus sin space alpha minus 1 plus sin space alpha over denominator 1 minus sin squared space alpha end fraction close parentheses end cell row blank equals cell cos squared alpha open parentheses fraction numerator 2 sin space alpha over denominator cos squared space alpha end fraction close parentheses end cell row blank equals cell up diagonal strike cos squared alpha end strike open parentheses fraction numerator 2 sin space alpha over denominator up diagonal strike cos squared space alpha end strike end fraction close parentheses end cell row blank equals cell 2 sin space alpha end cell end table$

Dengan demikian terbukti bahwa $fraction numerator cos squared alpha over denominator 1 minus sin space alpha end fraction minus fraction numerator cos squared alpha over denominator 1 plus sin space alpha end fraction equals 2 space sin space alpha$ .