Himpunan penyelesaian dari sin 3x - sin x + cos 2x = 0 , 0< x < 360 .....

[tex]u=\sin{(x)}\\\\\sin{(3x)}=\sin{(2x+x)}\\=\sin{(2x)}\cos{(x)}+\sin{(x)}\cos{(2x)}\\=2\sin{(x)}\cos^2{(x)}+\sin{(x)}\times(1-2\sin^2{(x)})\\=2u(1-u^2)+u(1-2u^2)\\=2u-2u^3+u-2u^3\\=-4u^3+3u\\\\\sin{(3x)}-\sin{(x)}+\cos{(2x)}=-4u^3+3u-u+1-2u^2\\=-4u^3-2u^2+2u+1=0\\4u^3+2u^2-2u-1=0\\(2u+1)(2u^2-1)=0\\u_1=-\frac{1}{2}\rightarrow x_1=210^{\circ}, x_2=330^{\circ}\\u_2=\frac{1}{\sqrt{2}}\rightarrow x_3=45^{\circ},x_4=135^{\circ}\\u_3=-\frac{1}{\sqrt{2}}\rightarrow x_5=225^{\circ},x_6=315^{\circ}[/tex]