因数 sin^6(θ)+cos^6(θ)

解

因数

sin^{6} (θ) + cos^{6} (θ)

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

解答ステップ

sin^{6} (θ) + cos^{6} (θ)

sin^{6} (θ) + cos^{6} (θ)

を書き換え

(sin^{2} (θ))^{3} + (cos^{2} (θ))^{3}

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

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