54cos22x+(cos2x)2+(sin2x)2+(cos2x)3+(sin2x)3=2
54cos22x+(cos2x+sin2x)2−2sin2x⋅cos2x+(cos2x+sin2x)(sin4x+cos4x−sin2x⋅cos2x)=2
⇒54cos22x+1−2sin2x.cos2x+(sin4x+cos4x−sin2x⋅cos2x)=2
54cos22x+1−2sin2x.cos2x+(1−3sin2x⋅cos2x)=2
⇒54cos22x−5sin2x.cos2x=0
54−54sin22x−5sin2x⋅cos2x=0
⇒54−54sin22x−54sin22x=0
sin22x=12⇒sin2x=±1√2
∴x=π8,3π8,5π8,7π8,9π8,11π8,13π8,15π8
Hence number of solutions in the given interval is 8.