Pertanyaan

Buktikanlah identitas trigonometri berikut. a. 1 + tan 2 A 2 tan A = 2 sin A cos A

Buktikanlah identitas trigonometri berikut.

a. $\frac{2 tan A}{1 + tan ^{2} A} = 2 sin A cos A$

R. Novianto

Master Teacher

Mahasiswa/Alumni Universitas Tanjungpura Pontianak

Jawaban terverifikasi

Pembahasan

Untuk membuktikanidentitas trigonometri , maka rumus identitas yangdigunakan adalah Selanjutnya kita buktikan

Untuk membuktikan identitas trigonometri $begin mathsize 14px style fraction numerator 2 tan A over denominator 1 plus tan squared A end fraction equals 2 sin A cos A end style$ , maka rumus identitas yang digunakan adalah

$begin mathsize 14px style table attributes columnalign right center left columnspacing 2px end attributes row cell tan space straight A end cell equals cell fraction numerator sin space straight A over denominator cos space straight A end fraction end cell row blank blank blank row cell 1 plus tan squared straight A end cell equals cell sec squared straight A end cell row blank blank blank row cell sec space straight A end cell equals cell fraction numerator 1 over denominator cos space straight A end fraction end cell end table end style$

Selanjutnya kita buktikan

$begin mathsize 14px style table attributes columnalign right center left columnspacing 2px end attributes row cell fraction numerator 2 space tan space straight A over denominator 1 plus tan squared straight A end fraction end cell equals cell 2 space sin space straight A space cos space straight A end cell row cell fraction numerator 2 times open parentheses begin display style fraction numerator sin space straight A over denominator cos space straight A end fraction end style close parentheses over denominator sec squared space straight A end fraction end cell equals cell 2 space sin space straight A space cos space straight A end cell row cell fraction numerator 2 times open parentheses sin space straight A times begin display style fraction numerator 1 over denominator cos space straight A end fraction end style close parentheses over denominator open parentheses begin display style fraction numerator 1 over denominator cos squared space straight A end fraction end style close parentheses end fraction end cell equals cell 2 space sin space straight A space cos space straight A end cell row cell 2 space sin space straight A space fraction numerator cos squared straight A over denominator cos space straight A end fraction end cell equals cell 2 space sin space straight A space cos space straight A end cell row cell 2 space sin space straight A space cos space straight A end cell equals cell 2 space sin space straight A space cos space straight A space open parentheses terbukti close parentheses end cell end table end style$