a,
sin^{4}x+cos^{4}x=(sin^{2}x+cos^{2}x)^{2}-2sin^{2}x.cos^{2}x
=1-\frac{1}{2}sin^{2}2x=\frac{3}{4}+\frac{1}{4}(1-2sin^{2}2x)=\frac{3}{4}+\frac{1}{4}cos4x
e,
2sin^{2}(\frac{\pi }{4}-\frac{x}{2})=2.\frac{1-cos(\frac{\pi }{2}-\frac{x}{2})}{2}=1-sinx
m...