Pertanyaan

Buktikanlah identitas trigonometri berikut. sin 2 a ( 1 + cot 2 a ) = 1

Buktikanlah identitas trigonometri berikut.

$sin^{2} a (1 + cot^{2} a) = 1$

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Klaim

Y. Fathoni

Master Teacher

Mahasiswa/Alumni Universitas Negeri Yogyakarta.

Jawaban terverifikasi

Jawaban

terbukti bahwa .

terbukti bahwa begin mathsize 14px style sin squared space a open parentheses 1 plus cot squared space a close parentheses equals 1 end style

Pembahasan

Ingat identitas dan perbandingan trigonometri. Akan dibuktikan . Perhatikan perhitungan berikut. Jadi, terbukti bahwa .

Ingat identitas dan perbandingan trigonometri.

$table attributes columnalign right center left columnspacing 2px end attributes row cell sin squared space a plus cos squared space a end cell equals 1 row cell cot space a end cell equals cell fraction numerator cos space a over denominator sin space a end fraction end cell end table$

Akan dibuktikan begin mathsize 14px style sin squared space a open parentheses 1 plus cot squared space a close parentheses equals 1 end style .

Perhatikan perhitungan berikut.

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

Jadi, terbukti bahwa begin mathsize 14px style sin squared space a open parentheses 1 plus cot squared space a close parentheses equals 1 end style .