展開する (sin^4(x)+cos^4(x-1))(sec^2(x)+csc^2(x))

解

展開する

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

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

解答ステップ

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

FOIL メソッドを適用する:

(a + b) (c + d) = a c + a d + b c + b d

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

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