Pertanyaan

Jika sin ( A − a ) F = sin A W , buktikan bahwa tan A = W cos a − F W sin a .

Jika $\frac{F}{sin ( A - a )} = \frac{W}{sin A}$ , buktikan bahwa $tan A = \frac{W sin a}{W cos a - F}$ .

R. Febrianti

Master Teacher

Mahasiswa/Alumni Universitas Negeri Malang

Jawaban terverifikasi

Jawaban

berdasarkan hitungan di atasterbukti bahwa .

berdasarkan hitungan di atas terbukti bahwa $tan space text A end text equals fraction numerator text W end text space sin space a over denominator text W end text space cos space a minus text F end text end fraction$ .

Pembahasan

Ingat rumus selisihdua sudut pada sinus yaitu Sehingga dapat dijabarkan sebagai berikut. Jadi berdasarkan hitungan di atasterbukti bahwa .

Ingat rumus selisih dua sudut pada sinus yaitu

sin open parentheses text A end text minus text B end text close parentheses equals sin space text A end text times cos space text B end text minus cos space text A end text space sin space text B end text

Sehingga $fraction numerator text F end text over denominator sin open parentheses text A end text minus a close parentheses end fraction equals fraction numerator text W end text over denominator sin space text A end text end fraction$ dapat dijabarkan sebagai berikut.

$table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator text F end text over denominator sin open parentheses text A end text minus a close parentheses end fraction end cell equals cell fraction numerator text W end text over denominator sin space text A end text end fraction end cell row cell fraction numerator text F end text over denominator sin space text A end text space cos space a minus cos space text A end text space sin space a end fraction end cell equals cell fraction numerator text W end text over denominator sin space text A end text end fraction end cell row cell text F end text sin space A end cell equals cell text W end text sin space text A end text space cos space a minus text W end text cos space text A end text space sin space a end cell row cell text F end text sin space text A end text minus text W end text sin space text A end text space cos space a end cell equals cell negative text W end text cos space text A end text space sin space a end cell row cell sin space text A end text open parentheses text F end text minus text W end text cos space a close parentheses end cell equals cell negative text W end text cos space text A end text space sin space a end cell row cell fraction numerator sin space text A end text over denominator cos space text A end text end fraction open parentheses text F end text minus text W end text cos space a close parentheses end cell equals cell fraction numerator negative text W end text cos space text A end text space sin space a over denominator cos space text A end text end fraction end cell row cell tan space text A end text open parentheses text F end text minus text W end text cos space a close parentheses end cell equals cell negative text W end text space sin space a end cell row cell tan space text A end text end cell equals cell fraction numerator negative text W end text space sin space a over denominator text F end text minus text W end text cos space a end fraction end cell row cell tan space text A end text end cell equals cell fraction numerator negative text W end text space sin space a over denominator negative left parenthesis text W end text cos space a minus text F end text right parenthesis end fraction end cell row cell tan space text A end text end cell equals cell fraction numerator text W end text space sin space a over denominator text W end text cos space a minus text F end text end fraction end cell end table$

Jadi berdasarkan hitungan di atas terbukti bahwa $tan space text A end text equals fraction numerator text W end text space sin space a over denominator text W end text space cos space a minus text F end text end fraction$ .