✔ 最佳答案
2(sinx)^2- sin2x=2
2(sinx)^2 - 2 sinx cos x = 2
Dividing both sides by (cosx)^2,
2(tanx)^2-2tanx-2(secx)^2=0
(tanx)^2-tanx-[1+(tanx)^2]=0
tanx = -1
x = 135* or 315* for 0 < x < 360*
2008-01-17 23:21:42 補充:
Remark: 1 + (tanx)^2 = (secx)^2
2008-01-18 13:32:41 補充:
抱歉, 這個方法是會解漏了兩個根的, 正確部驟如下:2(sinx)^2- sin2x = 22[ 1 - (cosx)^2 ] - 2 sin x cos x = 21 - (cosx)^2 - sinxcosx = 1-cos x ( cos x + sin x ) = 0 cos x = 0 or tan x = -1 x = 90*, 270*, 135*, 315* for 0 < x < 360*
2008-01-18 13:36:40 補充:
下面那位有兩處錯了:( 1 ) sin^2 x = ( sin x )^2 這樣表示是為免與sin 2x混淆( 2 ) 0*, 180* 不是cos x = 0 的根, 代回原式便可得知:2(sin0)^2 - sin2(0) = 0 - 0 = 0 不等於22(sin180*)^2 - sin2(180*) = 0 - 0 = 0 不等於2
2008-01-18 13:42:18 補充:
To下面再下面那位:題目是要解方程而不是求方程的通解呀!