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Diketahui sin α cos β = 3 1 dan ( α + β ) = 6 5 π . Nilai sin(α - β) = ....

Diketahui $sin α cos β = \frac{1}{3}$ dan $(α + β) = \frac{5 π}{6}$ . Nilai sin(α - β) = ....

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$begin mathsize 14px inline style bold i bold right parenthesis bold space Jabarkan space bentuk space sin invisible function application left parenthesis straight alpha minus straight beta right parenthesis sin invisible function application open parentheses straight alpha minus straight beta close parentheses equals sin invisible function application space straight alpha space cos space invisible function application straight beta minus cos space invisible function application straight alpha space sin invisible function application space straight beta sin invisible function application open parentheses straight alpha minus straight beta close parentheses equals 1 third minus cos space invisible function application straight alpha space sin space invisible function application straight beta bold ii bold right parenthesis bold space Cari space nilai space cos space invisible function application straight alpha space space sin space invisible function application straight beta space menggunakan space sin invisible function application left parenthesis straight alpha plus straight beta right parenthesis sin invisible function application open parentheses straight alpha plus straight beta close parentheses equals sin space invisible function application straight alpha space cos space invisible function application straight beta plus cos space invisible function application straight alpha space sin invisible function application space straight beta sin invisible function application fraction numerator 5 straight pi over denominator 6 end fraction equals 1 third plus cos space invisible function application straight alpha space sin space invisible function application straight beta 1 half equals 1 third plus cos space invisible function application straight alpha space sin space invisible function application straight beta cos space invisible function application straight alpha space sin invisible function application space straight beta equals 1 half minus 1 third cos space invisible function application straight alpha space sin space invisible function application straight beta equals 1 over 6 bold iii bold right parenthesis bold space Substitusi space ke space persamaan space awal sin invisible function application open parentheses straight alpha minus straight beta close parentheses equals 1 third minus cos space invisible function application straight alpha space sin space invisible function application straight beta sin invisible function application open parentheses straight alpha minus straight beta close parentheses equals 1 third minus 1 over 6 sin invisible function application open parentheses straight alpha minus straight beta close parentheses equals 1 over 6 end style$