\(3\sin^2\left(180-x\right)+2\sin\left(90+x\right)\cos\left(90+x\right)-5\sin^2\left(270+x\right)=0\)

\(\sin3x=2\sin^3x\)

\(\cos^3x-4\sin^3x-3\cos x\sin^2x+\sin x=0\)

\(4\sin^3x+3\cos^3x-3\sin x-\sin^2x\cos x=0\)

\(3\sin^3x+4\cos^3x=3\sin x\)

\(2\sin\left(\frac{\pi}{4}+x\right)+\sin\left(x-\frac{\pi}{4}\right)=\frac{3\sqrt{2}}{2}\)

\(\sin^2x+\sqrt{6}\cos x=3\cos^2x+\sqrt{2}s\text{inx}\)

\(\sin3x+\sqrt{3}\cos3x=2\sin\left(x+\frac{\pi}{3}\right)\)

\(2\cos\left(x+\frac{\pi}{6}\right)+3\cos\left(x+\frac{\pi}{3}\right)=2\)

\(2\sin^2x+\sqrt{3}\sin2x=\sqrt{3}\)