Pertanyaan

Diketahui cos ( α − β ) = 3 5 dan cos α cos β = 2 3 , α dan β sudt lancip. Nilai tan α tan β adalah ....

Diketahui $cos (α - β) = \frac{5}{3}$ dan $cos α cos β = \frac{3}{2}$ , $α dan β$ sudt lancip. Nilai $tan α tan β$ adalah ....

Y. Endah

Master Teacher

Mahasiswa/Alumni Institut Teknologi Bandung

Jawaban terverifikasi

Pembahasan

Perhatikan sehingga jadi, diperoleh .

Perhatikan

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell cos space open parentheses alpha minus beta close parentheses end cell equals cell cos space alpha space cos space beta plus sin space alpha space sin space beta end cell row cell 5 over 3 end cell equals cell 3 over 2 plus sin space alpha space sin space beta end cell row cell sin space alpha space sin space beta end cell equals cell 5 over 3 minus 3 over 2 end cell row cell sin space alpha space sin space beta end cell equals cell fraction numerator 10 minus 9 over denominator 6 end fraction end cell row cell sin space alpha space sin space beta end cell equals cell 1 over 6 end cell end table end style$

sehingga

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell tan space alpha space tan space beta end cell equals cell fraction numerator sin space alpha space sin space beta over denominator cos space alpha space cos space beta end fraction end cell row cell tan space alpha space tan space beta end cell equals cell fraction numerator begin display style 1 over 6 end style over denominator begin display style 3 over 2 end style end fraction end cell row cell tan space alpha space tan space beta end cell equals cell 1 over 6 times 2 over 3 end cell row cell tan space alpha space tan space beta end cell equals cell 1 over 9 end cell end table end style$

jadi, diperoleh .