выразить sin^4a+cos^4a через cos4a

sin^{4} \alpha + cos^{4} \alpha = ( sin^{2} \alpha )^{2} + ( cos^{2} \alpha )^{2} = ( \frac{1 - cos 2 \alpha }{2} )^{2} + ( \frac{1 + cos2 \alpha }{2} )^{2} = \\ \frac{1 - 2cos2 \alpha + cos^{2}2 \alpha }{4} + \frac{1 + 2cos2 \alpha + cos^{2}2 \alpha }{4} = \\ \frac{1 - 2cos2 \alpha + cos^{2} 2 \alpha + 1 + 2cos2 \alpha + cos^{2} 2 \alpha }{4} = \frac{2 cos^{2} 2 \alpha + 2}{4} = \frac{ cos^{2} 2 \alpha + 1}{2} = \frac{ \frac{1 + cos4 \alpha }{2} +1}{2} = \frac{1 + cos4 \alpha + 2}{4} = \frac{1}{4} cos4 \alpha + \frac{3}{4}