find the general solution of the following in degrees:
tan 2x tan x = 1
the ans is 180 +- 30
urgent add maths
2007-03-09 6:41 am
回答 (2)
2007-03-09 6:45 am
✔ 最佳答案
tan2x=2tanx/(1-tan^2x)So
tan 2x tan x = 1
2tan^2x/(1-tan^2x)=1
2tan^2x=1-tan^2x
3tan^2x=1
tan^2x=1/3
tanx=√1/3 or -√1/3
x=180n+30 or 180n-30
2007-03-08 22:49:11 補充：
補充問題說找general solution 所以答案應該有個ｎ（ｎ是整數）
2007-03-09 6:47 am
tan 2x tan x = 1
[2 tan x / (1 - tan^2 x)] tan x = 1
2 tan^2 x = 1 - tan^2 x
tan^2 x = 1/3
tan x = sqrt3 / 3
x = 180n +- 30
[2 tan x / (1 - tan^2 x)] tan x = 1
2 tan^2 x = 1 - tan^2 x
tan^2 x = 1/3
tan x = sqrt3 / 3
x = 180n +- 30
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