Pertanyaan

Jika tan A = 5 12 dan A − B = 22 5 ∘ ,maka tan B = ....

Jika $tan A = \frac{12}{5}$ dan $A - B = 22 5^{\circ}$ , maka $tan B =$ ....

M. Mariyam

Master Teacher

Mahasiswa/Alumni Institut Pertanian Bogor

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah A.

Pembahasan

Ingat bahwa Sehingga Ingat bahwa tan( 180° + x) = tan x , sehingga Jadi, jawaban yang tepat adalah A.

Ingat bahwa

$begin mathsize 14px style tan invisible function application open parentheses A minus B close parentheses equals fraction numerator tan invisible function application A minus tan invisible function application B over denominator 1 plus tan invisible function application A tan invisible function application B end fraction end style$

Sehingga

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell tan invisible function application open parentheses A minus B close parentheses end cell equals cell fraction numerator tan invisible function application A minus tan invisible function application B over denominator 1 plus tan invisible function application A tan invisible function application B end fraction end cell row cell tan invisible function application 225 degree end cell equals cell fraction numerator 12 over 5 minus tan invisible function application B over denominator 1 plus 12 over 5 times tan invisible function application B end fraction end cell row cell tan invisible function application open parentheses 180 degree plus 45 degree close parentheses end cell equals cell fraction numerator 12 over 5 minus tan invisible function application B over denominator 1 plus 12 over 5 times tan invisible function application B end fraction end cell row blank blank blank row blank blank blank row blank blank blank end table end style$

Ingat bahwa tan(180° + x) = tan x , sehingga

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell tan invisible function application open parentheses 180 degree plus 45 degree close parentheses end cell equals cell fraction numerator 12 over 5 minus tan invisible function application B over denominator 1 plus 12 over 5 times tan invisible function application B end fraction end cell row cell tan invisible function application 45 degree end cell equals cell fraction numerator 12 over 5 minus tan invisible function application B over denominator 1 plus 12 over 5 times tan invisible function application B end fraction end cell row 1 equals cell fraction numerator 12 over 5 minus tan invisible function application B over denominator 1 plus 12 over 5 times tan invisible function application B end fraction end cell row cell 1 plus 12 over 5 times tan invisible function application B end cell equals cell 12 over 5 minus tan invisible function application B end cell row cell 5 plus 12 tan invisible function application B end cell equals cell 12 minus 5 tan invisible function application B end cell row cell 12 tan invisible function application B plus 5 tan invisible function application B end cell equals cell 12 minus 5 end cell row cell 17 tan invisible function application B end cell equals 7 row cell tan invisible function application B end cell equals cell 7 over 17 end cell end table end style$

Jadi, jawaban yang tepat adalah A.