\(2 \sin ^{6} x-3 \sin ^{4} x+1=3 \cos ^{4} x-2 \cos ^{6} x \Leftrightarrow 2\left(\sin ^{6} x+\cos ^{6} x\right)+1=3 \sin ^{4} x+3 \cos ^{4} x\)

\(\Leftrightarrow 2\left[\left(\sin ^{2} x+\cos ^{2} x\right)\left(\sin ^{4} x-\sin ^{2} x \cdot \cos ^{2} x+\cos ^{4} x\right)\right]+1=3 \sin ^{4} x+3 \cos ^{4} x\)

\(\Leftrightarrow 2 \sin ^{4} x-2 \sin ^{2} x \cdot \cos ^{2} x+2 \cos s^{4} x+1=3 \sin ^{4} x+3 \cos ^{4} x \Leftrightarrow 1=\left(\sin ^{2} x+\cos ^{2} x\right)^{2}\)