\(\Leftrightarrow cos^4x+sin^4x+\dfrac{1}{2}\left[sin\left(3x-\dfrac{pi}{4}+x-\dfrac{pi}{4}\right)+sin\left(3x-\dfrac{pi}{4}-x+\dfrac{pi}{4}\right)\right]-\dfrac{3}{2}=0\)
\(\Leftrightarrow1-\dfrac{1}{2}sin^22x+\dfrac{1}{2}\left[sin\left(4x-\dfrac{pi}{2}\right)+sin2x\right]-\dfrac{3}{2}=0\)
=>\(-\dfrac{1}{2}sin^22x-\dfrac{1}{2}+\dfrac{1}{2}\left[-sin\left(\dfrac{pi}{2}-4x\right)+sin2x\right]=0\)
=>\(-sin^22x-1-cos4x+sin2x=0\)
=>\(-sin^22x-1-\left(1-2sin^22x\right)+sin2x=0\)
=>\(-sin^22x-1-1+2sin^22x+sin2x=0\)
=>\(sin^22x+sin2x-2=0\)
=>sin2x-1=0
=>sin2x=1
=>2x=pi/2+k2pi
=>x=pi/4+kpi
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