展開する (sin^{(4)}(θ)-cos^{(4)}(θ)+1)csc^2(x)

解

展開する

(sin^{(4)} (θ) - cos^{(4)} (θ) + 1) csc^{2} (x)

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

解答ステップ

(sin^{4} (θ) - cos^{4} (θ) + 1) csc^{2} (x)

= csc^{2} (x) (sin^{4} (θ) - cos^{4} (θ) + 1)

分配法則を適用する:

m (a + b + c) = ma + mb + m c

csc^{2} (x) (sin^{4} (θ) - cos^{4} (θ) + 1) = csc^{2} (x) sin^{4} (θ) + csc^{2} (x) (- cos^{4} (θ)) + csc^{2} (x) \cdot 1

= csc^{2} (x) sin^{4} (θ) + csc^{2} (x) (- cos^{4} (θ)) + csc^{2} (x) \cdot 1

簡素化

csc^{2} (x) sin^{4} (θ) + csc^{2} (x) (- cos^{4} (θ)) + csc^{2} (x) \cdot 1 : csc^{2} (x) sin^{4} (θ) - csc^{2} (x) cos^{4} (θ) + csc^{2} (x)

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