簡約 (e^{-iw}-1)^2(e^{iw}-1)^2

解

簡約

(e^{- i w} - 1)^{2} (e^{i w} - 1)^{2}

sin^{4} (w) + 2 sin^{2} (w) + 2 sin^{2} (w) cos^{2} (w) - 4 sin^{2} (w) cos (w) + cos^{4} (w) - 4 cos^{3} (w) + 6 cos^{2} (w) - 4 cos (w) + 1

解答ステップ

(e^{- i w} - 1)^{2} (e^{i w} - 1)^{2}

(e^{- i w} - 1)^{2} = (cos (w) - i sin (w) - 1)^{2}

= (cos (w) - i sin (w) - 1)^{2} (e^{i w} - 1)^{2}

(e^{i w} - 1)^{2} = (cos (w) + i sin (w) - 1)^{2}

= (cos (w) - i sin (w) - 1)^{2} (cos (w) + i sin (w) - 1)^{2}

= (cos (w) - i sin (w) - 1)^{2} (cos (w) + i sin (w) - 1)^{2}

(cos (w) - i sin (w) - 1)^{2} = (cos (w) - i sin (w) - 1) (cos (w) - i sin (w) - 1)

= (cos (w) - i sin (w) - 1) (cos (w) - i sin (w) - 1) (cos (w) + i sin (w) - 1)^{2}

(cos (w) + sin (w) i - 1)^{2} = (cos (w) + sin (w) i - 1) (cos (w) + sin (w) i - 1)

= (cos (w) - i sin (w) - 1) (cos (w) - i sin (w) - 1) (cos (w) + i sin (w) - 1) (cos (w) + i sin (w) - 1)

拡張

(cos (w) - i sin (w) - 1) (cos (w) - i sin (w) - 1) (cos (w) + sin (w) i - 1) (cos (w) + sin (w) i - 1) : sin^{4} (w) + 2 sin^{2} (w) + 2 sin^{2} (w) cos^{2} (w) - 4 sin^{2} (w) cos (w) + cos^{4} (w) - 4 cos^{3} (w) + 6 cos^{2} (w) - 4 cos (w) + 1

= sin^{4} (w) + 2 sin^{2} (w) + 2 sin^{2} (w) cos^{2} (w) - 4 sin^{2} (w) cos (w) + cos^{4} (w) - 4 cos^{3} (w) + 6 cos^{2} (w) - 4 cos (w) + 1