Pertanyaan

Diketahui 2 sin 2 θ − cos 2 θ = 1 . Tunjukkan bahwa tan 2 θ = 2

Diketahui $2 sin^{2} θ - cos^{2} θ = 1$ .
Tunjukkan bahwa $tan^{2} θ = 2$

S. Difhayanti

Master Teacher

Mahasiswa/Alumni Universitas Muhammadiyah Prof. Dr. Hamka

Jawaban terverifikasi

Jawaban

dapat ditunjukkanbahwa jika diketahui .

dapat ditunjukkan bahwa tan squared space theta equals 2

jika diketahui 2 space sin squared space theta minus cos squared space theta equals 1

Pembahasan

Ingat kembali identitas dasar trigonometri berikut. Jika , maka dapat ditunjukkan seperti berikut ini. Jadi, dapat ditunjukkanbahwa jika diketahui .

Ingat kembali identitas dasar trigonometri berikut.

$table attributes columnalign right center left columnspacing 0px end attributes row cell sin squared space theta plus cos squared space theta end cell equals 1 row cell tan space theta end cell equals cell fraction numerator sin space theta over denominator cos space theta end fraction end cell end table$

Jika 2 space sin squared space theta minus cos squared space theta equals 1 , maka dapat ditunjukkan tan squared space theta equals 2 seperti berikut ini.

$table attributes columnalign right center left columnspacing 0px end attributes row cell 2 space sin squared space theta minus cos squared space theta end cell equals 1 row cell 2 space sin squared space theta minus cos squared space theta end cell equals cell sin squared space theta minus cos squared space theta end cell row cell 2 space sin squared space theta minus sin squared space theta end cell equals cell cos squared space theta plus cos squared space theta end cell row cell sin squared space theta end cell equals cell 2 space cos squared space theta end cell row cell fraction numerator sin squared space theta over denominator cos squared space theta end fraction end cell equals 2 row cell tan squared space theta end cell equals cell 2 space open parentheses Terbukti close parentheses end cell end table$

Jadi, dapat ditunjukkan bahwa tan squared space theta equals 2 jika diketahui 2 space sin squared space theta minus cos squared space theta equals 1 .