Pertanyaan

Buktikan identitas trigonometri berikut. tan 2 x = 1 − cos 2 x ( 1 + tan 2 x )

Buktikan identitas trigonometri berikut.

$tan^{2} x = 1 - cos 2 x (1 + tan^{2} x)$

H. Eka

Master Teacher

Mahasiswa/Alumni Universitas Pendidikan Indonesia

Jawaban terverifikasi

Jawaban

terbukti bahwa

terbukti bahwa tan squared space x equals 1 minus cos space 2 x open parentheses 1 plus tan squared space x close parentheses

Pembahasan

Identitas trigonometri: Bukti dari identitas trigonometri tersebut adalah sebagai berikut. Dengan demikian, terbukti bahwa

Identitas trigonometri:

tan squared space alpha plus 1 equals s e c squared space alpha

cos space 2 alpha equals 1 minus 2 space sin squared space alpha

Bukti dari identitas trigonometri tersebut adalah sebagai berikut.

$table attributes columnalign right center left columnspacing 0px end attributes row cell tan squared space x end cell equals cell 1 minus cos space 2 x open parentheses 1 plus tan squared space x close parentheses end cell row cell tan squared space x end cell equals cell 1 minus open parentheses 1 minus 2 space sin squared space x close parentheses open parentheses 1 plus tan squared space x close parentheses end cell row cell tan squared space x end cell equals cell 1 minus open parentheses 1 minus 2 space sin squared space x close parentheses open parentheses text sec end text squared space x close parentheses end cell row cell tan squared space x end cell equals cell 1 minus open parentheses s e c squared space x minus 2 space sin squared space x times s e c squared space x close parentheses end cell row cell tan squared space x end cell equals cell 1 minus open parentheses s e c squared space x minus 2 space sin squared space x times fraction numerator 1 over denominator cos squared space x end fraction close parentheses end cell row cell tan squared space x end cell equals cell 1 minus open parentheses s e c squared space x minus 2 space tan squared space x close parentheses end cell row cell tan squared space x end cell equals cell 1 minus s e c squared space x plus 2 space tan squared space x end cell row cell tan squared space x end cell equals cell negative tan squared space x plus 2 space tan squared space x end cell row cell tan squared space x end cell equals cell tan squared space x end cell end table$

Dengan demikian, terbukti bahwa tan squared space x equals 1 minus cos space 2 x open parentheses 1 plus tan squared space x close parentheses