Pertanyaan

cot α 2 sin α ⋅ cos α + sec 2 α 2 = ....

$\frac{2 sin α \cdot cos α}{cot α} + \frac{2}{sec ^{2} α} = ....$

Y. Fathoni

Master Teacher

Mahasiswa/Alumni Universitas Negeri Yogyakarta.

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah E.

Pembahasan

Gunakan konsep definisi cotangen dan secan, dan identitas trigonometri. Perhatikan perhitungan berikut. Diperoleh nilai . Jadi, jawaban yang tepat adalah E.

Gunakan konsep definisi cotangen dan secan, dan identitas trigonometri.

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

Perhatikan perhitungan berikut.

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

Diperoleh nilai $begin mathsize 14px style fraction numerator 2 space sin space alpha times cos space alpha over denominator cot space alpha end fraction plus fraction numerator 2 over denominator sec squared space alpha end fraction equals 2 end style$ .

Jadi, jawaban yang tepat adalah E.