sin 3x + sin 2x - sin x = 4sin x * ((cos x)/2)
sin 3x = 3sin x - 4sin^3
sin 2x = 2sin x * cos
3sin x - 4sin^3 x + 2sin x * cos x - sin x =
(3sin x - 4sin^3 x + 2sin x * cos x - sin x)
We can simplify the equation with sin x, but we must make sure that we do not miss the case sin x = 0. When we simplify with sin x in the case sin x โ 0, we get:
2 + 2cos x - 4sin^2 x = 2cos x * (cos 3x)/2
Let's expand the right side:
2cos x * (cos 3x)/2 = cos x * cos 3x
Using cosine expansion, cos 3x:
cos 3x = 4cos^3 x - 3cos x
If we substitute this expression:
2 + 2cos x - 4sin^2 x =cos x(4 cos^ 3
It may be necessary to examine these expressions in more detail later, but the important thing is to examine the equation under a corner case. In the first case, when sin x = 0, we can solve sinx = 0 โ x = n.
Solution:
โ
x = ฮทฯ, NEZ
I think this is x
