Math Problem

(sin x)^2 – sin x cos x = 0
sin x sin x - sin x cos x = 0
sin x (sin x – cos x) = 0
Therefore sin x = 0 or (sin x – cos x) = 0
When sin x = 0, x = 0 deg , 180 deg, 360 deg

Sin x – cos x = 0
Sin x = cos x
Sin x/cos x = 1
tan x = 1
When tan x = 1, x = 45 deg , 225 deg

For the range 0 deg <= x <= 360 deg

x = 0 deg , 45 deg 180 deg, 225 deg or 360 deg (answer)

Since the range is given in degrees, the answer should be in degrees.

No offence to 回答者：karf：
x is in radians
If x = pi/2 or 3pi/2, then cos pi/2 = 0 or cos 3pi/2 = 0
You will have division by zero. That is not defined.
(sin x)^2/cosx = sin x
(1^2)/0 = 1

(sinx)^2/cosx = sinx
(sinx)^2 = sinx cosx
(sinx)^2 - sinx cosx = 0
sinx (sinx - cosx) = 0
sinx = 0 or sinx = cosx
x = pi/2 or 3pi/2 or pi/4 or 5pi/4

2011-12-07 11:16:46 補充：
(sinx)^2 / cosx = sinx
(sinx)^2 = sinx cosx
(sinx)^2 - sinx cosx = 0
sinx (sinx - cosx) = 0
sinx = 0 or sinx = cosx
x = pi/2 or 3pi/2 or pi/4 or 5pi/4