三角學解方程問題

sin x sin2x+ sin2xsin4x = sin3xsin4x
(-1/2) [ cos 3x - cos x ] + (-1/2) [ cos 6x - cos 2x ] = (-1/2) [ cos 7x - cos x ]
cos 3x - cos x + cos 6x - cos 2x = cos 7x - cos x
cos 3x - cos 2x = cos 7x - cos 6x
cos(2.5x+ 0.5x) - cos (2.5x - 0.5x) = cos (6.5x + 0.5x) - cos (6.5x - 0.5x)
-2sin 2.5x sin 0.5x = -2sin 6.5x sin 0.5x
(sin 6.5x - sin 2.5x)sin 0.5x = 0
[ cos (90-6.5x) - cos (90-2.5x) ] sin 0.5x = 0
[ cos ( 90-4.5x + (-2x) ) - cos ( 90-4.5x - (-2x) ) ] sin 0.5x = 0
-2 sin(90-4.5x) sin(-2x) sin 0.5x = 0
-2 cos 4.5x (-sin 2x) sin 0.5x = 0
cos 4.5x sin 2x sin 0.5x = 0
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cos 4.5x = 0
or sin 2x = 0 (rej. ∵ 0 < 2x < 180)
or sin 0.5x = 0 (rej. ∵ 0 < 0.5x < 45)
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4.5x = 90 or 270 ( 0 < 4.5x < 405 )
x = 20 or 60
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如果只能用那條恆等式就這樣做 (強行- -
若能使用其他積化和差 and 和差化積 就將果幾行 2.5x+0.5x ~ 6.5x+0.5x~
轉返做相對既公式-.-