Matematika

Pertanyaan

kak bantuin dong pakai cara yaa 15 dan 16
kak bantuin dong pakai cara yaa 15 dan 16

1 Jawaban

  • 15.
    sin² 45 = (¹/₂ √2)² = 1/2
    sin² 60 = (¹/₂ √3)² = 3/4
    cos² 45 = (¹/₂ √2)² = 1/2
    cos² 60 =( ¹/₂)²  =1/4
    tan 30 = 1/√3
    tan 60 = √3

    (sin² 45 .sin² 60 + cos² 45  cos² 60) / tan 30 . tan 60 =
    = (1/2 x 3/.4 + 1/2 x 1/4) / (1/√3)(√3)
    = ( 3/8 + 1/8)/ (1)
    = 4/8
    = 1/2

    16.

    (sin 270 . cos 135 - tan 135) / ( sin 150. cos 225) =
    = { (-1)(-1/2 √2)  - (-1) } / ( 1/2 √3)(- 1/2 √2)
    =  (1/2 √ 2  + 1) / ( -1/4 √6) ...kalikn 4√6 / 4√6
    = (1/2 √ 2 + 1)(4√6) / (-1/4 √6)(4√6)
    = (2√12 +  4√6)/ (-6)
    = ( 2 (2√3) + 4√6) / (-6)
     = (4√3 + 4√6) / -6
     = -4/6 (√3 + √6)
    = - 2/3 (√3 + √6)