Find the general solution of the equation
1) sin5xsinx + cos4xcos2x =0
-1/2(cos6x -cos4x) + 1/2(cos6x + cos2x) =0
-cos6x + cos4x + cos6x + cos2x =0
cos4x + cos2x =0
2cos^2x-1 + cos 2x =0
(2cos2x-1)(cos2x+1)
cos2x = 1/2 or cos2x =-1
2x=360n +/-(60) or 2x =360n+/-(180)
x= 180n+/-(30) or x=180n+/-(90)
不過我的答案是錯的~~WHY?????
2) tanx + tan (45 +x) =2
3) cot x + cot (兀/3-x) = -√3 <--express in radian
2&3 題完全不懂, 請幫忙!!!
compound angle (maths)
2013-09-26 2:23 am
回答 (2)
2013-09-26 4:28 pm
✔ 最佳答案
1) Sorry, I don't see any mistake. What is the correct answer?2) Let tan x = y, the equation becomes
y + (1 + y)/(1 - y) = 2
y(1 - y) + (1 + y) = 2(1 - y)
y - y^2 + 1 + y - 2 + 2y = 0
y^2 - 4y + 1 = 0
y = 2 +/- sqrt 3
that is tan x = 2 + sqrt 3 or 2 - sqrt 3
x = 5π/12 or π/12
= nπ + 5π/12 or nπ + π/12.
2013-09-26 08:43:04 補充：
(3) Let tan x = y, the equation becomes
1/y + (1 + sqrt 3 y)/(sqrt 3 - y) = - sqrt 3
(sqrt 3 - y) + y(1 + sqrt 3 y) = - sqrt 3 y (sqrt 3 - y)
sqrt 3 - y + y + sqrt 3 y^2 = - 3 y + sqrt 3 y^2
3y = sqrt 3
y = sqrt 3/3
so x = arctan ( sqrt 3/3) = π/6
x = n π + π/6.
2013-09-26 6:08 pm
x = 180n +/- 90 即是 x = 90(2n +/- 1), 因 n 是整數, 所以亦即 x = 90(2n -1)
你的答案是對的，寫法不同吧。[應該用簡單的一個，即 x = 90(2n - 1)。]
你的答案是對的，寫法不同吧。[應該用簡單的一個，即 x = 90(2n - 1)。]
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