因数 sin^6(a)+cos^6(a)

解

因数

sin^{6} (a) + cos^{6} (a)

(sin^{2} (a) + cos^{2} (a)) (sin^{4} (a) - cos^{2} (a) sin^{2} (a) + cos^{4} (a))

解答ステップ

sin^{6} (a) + cos^{6} (a)

sin^{6} (a) + cos^{6} (a)

を書き換え

(sin^{2} (a))^{3} + (cos^{2} (a))^{3}

= (sin^{2} (a))^{3} + (cos^{2} (a))^{3}

立方数の和の公式を適用する:

x^{3} + y^{3} = (x + y) (x^{2} - x y + y^{2})

(sin^{2} (a))^{3} + (cos^{2} (a))^{3} = (sin^{2} (a) + cos^{2} (a)) (sin^{4} (a) - cos^{2} (a) sin^{2} (a) + cos^{4} (a))

= (cos^{2} (a) + sin^{2} (a)) (cos^{4} (a) - cos^{2} (a) sin^{2} (a) + sin^{4} (a))