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

解

展開する

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

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

解答ステップ

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

分配法則を適用する:

a (b + c) = ab + a c

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

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

簡素化

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

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