A-maths問題

tan2x(tanx) = 1
tan2x = (tanx + tanx) / (1 - tanX(tanx))
= 2tanx / (1 - (tanx)^2)

tan2x(tanx) = 1
[2tanx / (1 - (tanx)^2)](tanx) = 1
2(tanx)^2 = 1 - (tanx)^2
3(tanx)^2 = 1
tanx = + sqrt(1/3) or tanx = - sqrt(1/3)
(note: sqrt = square root)

x = 30' 150' 210' 330'

x = (180n - 30) or (180n + 30) or (360n + 30) or (360n - 30)

tanXtan2X = 1
(sinX/cosX)(sin2X/cos2X) = 1
sinXsin2X = cosXcos2X
cosXcos2X-cos3X = cosXcos2X
cos3X = 0

Therefore,
3X = 360* x n + 90*
X = 120* x n + 30* where n is integer