Pertanyaan

Buktikan jika sin β ⋅ tan β + cos β = sec β .

Buktikan jika $sin β \cdot tan β + cos β = sec β$ .

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Habis dalam

Klaim

D. Kamilia

Master Teacher

Mahasiswa/Alumni Universitas Negeri Malang

Jawaban terverifikasi

Jawaban

terbukti bahwa .

terbukti bahwa sin space beta times tan space beta plus cos space beta equals sec space beta

Pembahasan

Gunakan identitas dan perbandingan trigonometri untuk membuktikan. Perhtikan perhitungan berikut. Jadi, terbukti bahwa .

Gunakan identitas dan perbandingan trigonometri untuk membuktikan.

$table attributes columnalign right center left columnspacing 2px end attributes row cell sin squared space beta plus cos squared space beta end cell equals 1 row cell tan space beta end cell equals cell fraction numerator sin space beta over denominator cos space beta end fraction end cell row cell sec space beta end cell equals cell fraction numerator 1 over denominator cos space beta end fraction end cell end table$

Perhtikan perhitungan berikut.

$table attributes columnalign right center left columnspacing 2px end attributes row cell sin space beta times tan space beta plus cos space beta end cell equals cell sin space beta times fraction numerator sin space beta over denominator cos space beta end fraction plus cos space beta end cell row blank equals cell fraction numerator sin squared space beta over denominator cos space beta end fraction plus cos space beta end cell row blank equals cell fraction numerator sin squared space beta plus cos squared space beta over denominator cos space beta end fraction end cell row blank equals cell fraction numerator 1 over denominator cos space beta end fraction end cell row cell sin space beta times tan space beta plus cos space beta end cell equals cell sec space beta end cell end table$

Jadi, terbukti bahwa sin space beta times tan space beta plus cos space beta equals sec space beta .