Matematika

Pertanyaan

tolong di bantu yaah
tolong di bantu yaah

1 Jawaban

  • cos β = 3/5 .... sin β = 4/5
    sin α = - ⅔... cos α = -√5/3
    tg α = 2√5 /5
    tg β = 4/3

    a) = sin α cos β + cos α sin β
    = (-⅔) ³/5 + (-√5/3) 4/5
    = (-6 - 4√5) / 15
    = - (6 + 4√5) / 15

    b) = cos α cos β + sin α sin β
    = (-√5/3) ³/5 + (-⅔) 4/5
    = (-3√5-8) /15
    = - (3√5 + 8) / 15

    c) = (tg α - tg β) / (1 + tg α tg β)
    = (2√5/5 - 4/3)/ (1 + 2√5/5. 4/3)
    = (6√5-20) / (15 + 8√5)
    = (6√5-20)(15-8√5) / (15²- (8√5)²)
    = 90√5-240-300+160√5 / (225-320)
    = 250√5 - 540 / -95
    = 540+250√5 / 95
    = (108 + 50√5) / 19