Tunjukkan bahwa: d. cos A cos Bsin (A−B)=tan A−tan B

Pertanyaan

Tunjukkan bahwa:

d. $fraction numerator sin space open parentheses A minus B close parentheses over denominator cos space A space cos space B end fraction equals tan space A minus tan space B$

D. Rajib

Master Teacher

Mahasiswa/Alumni Universitas Muhammadiyah Malang

Jawaban terverifikasi

Jawaban

terbukti bahwa $fraction numerator sin space open parentheses A minus B close parentheses over denominator cos space A space cos space B end fraction equals tan space A minus tan space B$

Pembahasan

Akan dibuktikan $fraction numerator sin space open parentheses A minus B close parentheses over denominator cos space A space cos space B end fraction equals tan space A minus tan space B$

Ingat bahwa

$sin left parenthesis A minus B right parenthesis equals table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell sin space A space cos space B minus cos space A space sin end cell end table space B tan space x equals fraction numerator sin space x over denominator cos space x end fraction$

Diperhatikan

$table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator sin open parentheses A minus B close parentheses over denominator cos space A space cos space B end fraction end cell equals cell fraction numerator sin space A space cos space B minus cos space A space sin space B over denominator cos space A space cos space B end fraction end cell row blank equals cell fraction numerator sin space A space cos space B over denominator cos space A space cos space B end fraction minus fraction numerator cos space A space sin space B over denominator cos space A space cos space B end fraction end cell row blank equals cell fraction numerator sin space A over denominator cos space A end fraction minus fraction numerator sin space B over denominator cos space B end fraction end cell row blank equals cell tan space A minus tan space B end cell end table$

Dengan demikian, terbukti bahwa $fraction numerator sin space open parentheses A minus B close parentheses over denominator cos space A space cos space B end fraction equals tan space A minus tan space B$