Pertanyaan

Sederhanakanlah. tan 2 θ cos 2 θ + cot 2 θ sin 2 θ

Sederhanakanlah.

$tan^{2} θ cos^{2} θ + cot^{2} θ sin^{2} θ$

S. Difhayanti

Master Teacher

Mahasiswa/Alumni Universitas Muhammadiyah Prof. Dr. Hamka

Jawaban terverifikasi

Jawaban

sederhana dari adalah 1.

sederhana dari tan to the power of 2 space end exponent theta space cos squared theta plus cot squared space theta space sin squared space theta

adalah 1.

Pembahasan

Ingat kembali identitas dasar trigonometri berikut. Oleh karena itu, didapat Jadi, sederhana dari adalah 1.

Ingat kembali identitas dasar trigonometri berikut.

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

Oleh karena itu, didapat

$table attributes columnalign right center left columnspacing 0px end attributes row cell tan to the power of 2 space end exponent theta space cos squared theta plus cot squared space theta space sin squared space theta end cell equals cell fraction numerator sin squared space theta over denominator up diagonal strike space cos squared theta end strike end fraction times up diagonal strike space cos squared theta end strike plus fraction numerator space cos squared theta over denominator up diagonal strike sin squared space theta end strike end fraction times up diagonal strike sin squared space theta end strike end cell row blank equals cell sin squared space theta plus cos squared theta end cell row blank equals 1 end table$

Jadi, sederhana dari tan to the power of 2 space end exponent theta space cos squared theta plus cot squared space theta space sin squared space theta adalah 1.