Question

Jika x memenuhi 3sinxcosx-sinx-6cosx+2=0 maka cos 2x=

Answer 1

Misalkan :
sin x = a
cos x = b

3ab - a - 6b + 2 = 0
faktorkan
a + 6b - 3ab - 2 = 0
(a-2 ) (1-3b ) = 0
a = 2
sin x = 2 , salah , karena -1<sin x < 1
1 - 3b = 0
3b = 1
  b = 1/3
cos x = 1/3 , benar , karena -1 < cos x < 1

sin x = √(1 - cos²x)
         = √(1 - (1/3)²)
         = √(8/9)
         = 2/3 √2

cos 2x = cos²x - sin²x
           = (1/3)² - (2/3 √2)²
           = 1/9 - 4/9 (2)
           = 1/9 - 8/9
           = -7/9

Answer 2