Roboguru

Diketahui  dan ,  sudt lancip. Nilai  adalah ....

Pertanyaan

Diketahui begin mathsize 14px style cos space open parentheses alpha minus beta close parentheses equals 5 over 3 end style dan begin mathsize 14px style cos space alpha space cos space beta equals 3 over 2 end stylebegin mathsize 14px style straight alpha space dan space straight beta end style sudt lancip. Nilai begin mathsize 14px style tan space alpha space tan space beta end style adalah ....

Pembahasan Soal:

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 begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank tan end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank alpha end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank tan end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank beta end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 1 over 9 end cell end table end style

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 11 April 2021

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