a-maths~~~~~~`

如下:


圖片參考：http://i117.photobucket.com/albums/o61/billy_hywung/Oct07/Crazytrigo8.jpg

16^(cos²x+2sin²x)+4^(2cos²x)=40
16^(cos²x+2(1-cos²x))+4^(2cos²x)=40
16^(2-cos²x)+4^(2cos²x)=40
16^(2-cos²x)+16^(cos²x)=40 (since 4^2 = 16)
256．16^(-cos²x) + 16^(cos²x) = 40
256 + (16^(cos²x))^2 = 40．16^(cos²x)
(16^(cos²x))^2 - 40．16^(cos²x) + 256 = 0
(16^cos²x - 32)(16^cos²x - 8) = 0
16^cos²x = 32 or 8
2^(4cos²x) = 2^5 or 2^3
4cos²x = 5 or 3
cosx = rt(5)/2(rejected,-1< cosx<1), -rt(5)/2(rejected,-1< cosx<1), rt(3)/2 or -rt(3)/2
x = pi/6, 5pi/6, 7pi/6 or 11pi/6