Pertanyaan

Jawablah pertanyaan-pertanyan di bawah ini dengan benar! Buktikan Identitas trigonometri berikut. cos β sin β − sin β cos β = sin β cos β 2 sin 2 β − 1

Jawablah pertanyaan-pertanyan di bawah ini dengan benar!

Buktikan Identitas trigonometri berikut.

$\frac{sin β}{cos β} - \frac{cos β}{sin β} = \frac{2 sin ^{2} β - 1}{sin β cos β}$

F. Kurnia

Master Teacher

Mahasiswa/Alumni Universitas Jember

Jawaban terverifikasi

Jawaban

terbukti bahwa .

terbukti bahwa $begin mathsize 14px style fraction numerator sin beta over denominator cos beta end fraction minus fraction numerator cos beta over denominator sin beta end fraction equals fraction numerator 2 sin squared beta minus 1 over denominator sin beta cos beta end fraction end style$ .

Pembahasan

Akan dibuktikan Ingat Bahwa Jadi, terbukti bahwa .

Akan dibuktikan $begin mathsize 14px style fraction numerator sin beta over denominator cos beta end fraction minus fraction numerator cos beta over denominator sin beta end fraction equals fraction numerator 2 sin squared beta minus 1 over denominator sin beta cos beta end fraction end style$

Ingat Bahwa

$begin mathsize 14px style rightwards arrow fraction numerator sin beta over denominator cos beta end fraction minus fraction numerator cos beta over denominator sin beta end fraction equals fraction numerator sin squared beta minus cos squared beta over denominator sin beta cos beta end fraction equals fraction numerator sin squared beta minus cos squared beta plus 1 minus 1 over denominator sin beta cos beta end fraction equals fraction numerator sin squared beta minus cos squared beta plus sin squared beta plus cos squared beta minus 1 over denominator sin beta cos beta end fraction equals fraction numerator 2 sin squared beta minus 1 over denominator sin beta cos beta end fraction end style$

Jadi, terbukti bahwa $begin mathsize 14px style fraction numerator sin beta over denominator cos beta end fraction minus fraction numerator cos beta over denominator sin beta end fraction equals fraction numerator 2 sin squared beta minus 1 over denominator sin beta cos beta end fraction end style$ .