Use the half-angle identities.
[tex]\sin^2x=\dfrac{1-\cos2x}2[/tex]
[tex]\implies\sin^4x=\left(\dfrac{1-\cos2x}2\right)^2=\dfrac{1-2\cos2x+\cos^22x}4[/tex]
[tex]\cos^2x=\dfrac{1+\cos2x}2[/tex]
[tex]\implies\sin^4x=\dfrac{1-2\cos2x+\frac{1+\cos4x}2}4=\dfrac{3-4\cos2x+\cos4x}8[/tex]
