Pertanyaan

Buktikan hubungan identitas berikut! 1 + Cos α 1 + 1 − Cos α 1 = 2 Cosec 2 α

Buktikan hubungan identitas berikut!

$\frac{1}{1 + Cos α} + \frac{1}{1 - Cos α} = 2 Cosec^{2} α$

S. Difhayanti

Master Teacher

Mahasiswa/Alumni Universitas Muhammadiyah Prof. Dr. Hamka

Jawaban terverifikasi

Jawaban

dapat disimpulkan bahwa terbukti.

dapat disimpulkan bahwa $fraction numerator 1 over denominator 1 plus Cos blank straight alpha end fraction plus fraction numerator 1 over denominator 1 minus Cos blank straight alpha end fraction equals 2 Cosec squared alpha$ terbukti.

Pembahasan

Ingat kembaliidentitas pada trigonometri berikut. sin x 1 = csc x Sehingga, dapat dibuktikan seperti berikut ini. Jadi, dapat disimpulkan bahwa terbukti.

Ingat kembali identitas pada trigonometri berikut.

$\frac{1}{sin x} = csc x$

Sehingga, dapat dibuktikan seperti berikut ini.

$table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator 1 over denominator 1 plus Cos blank straight alpha end fraction plus fraction numerator 1 over denominator 1 minus Cos blank straight alpha end fraction end cell equals cell fraction numerator 1 minus Cos blank straight alpha plus 1 plus Cos blank straight alpha over denominator 1 minus Cos squared straight alpha end fraction end cell row blank equals cell fraction numerator 1 plus 1 minus Cos blank straight alpha plus Cos blank straight alpha over denominator 1 minus Cos squared straight alpha end fraction end cell row blank equals cell fraction numerator 2 over denominator 1 minus Cos squared straight alpha end fraction end cell row blank equals cell fraction numerator 2 over denominator Sin squared straight alpha end fraction end cell row blank equals cell 2 cross times fraction numerator 1 over denominator Sin squared straight alpha end fraction end cell row blank equals cell 2 cross times Cosec squared alpha end cell row blank equals cell 2 Cosec squared alpha end cell end table$

Jadi, dapat disimpulkan bahwa $fraction numerator 1 over denominator 1 plus Cos blank straight alpha end fraction plus fraction numerator 1 over denominator 1 minus Cos blank straight alpha end fraction equals 2 Cosec squared alpha$ terbukti.