Question

Cos x . cos 2x = 0,25 berapa nilai x? (dalam derajat)

Answer 1

Ingat bahwa cos2x = (2cos^2 x) - 1
atau = 1 - 2sin^2 x
maka
cosx(2cos^2 x - 1) = 1/4
2cos^3 x - cosx = 1/4
2cos^3 x - cosx - 1/4 = 0 (semua ruas dikali 4)
8cos^3 x - 4cosx - 1 = 0
(4cos^2 x - 2cosx - 1)(2cosx + 1) = 0
# 4cos^2 x - 2 cosx - 1 = 0
tidak vbisa difajktorkan, maka tidak mwmenuhi
# 2 cosx + 1 = 0
2 cosx = -1
cosx = -1/2
cosx = cos 120'
cosx = cosß
x = +- ß + k.360'
maka x = +-120' + (k.360')
x = +120' + 0 = 120'
atau
x = -120 + (1.360')
x = 240'

jika 0'x = {120',240'}
Semoga membantu :)