展開する (9cos(x)-cos(9x)*9)^2

解

展開する

(9 cos (x) - cos (9 x) \cdot 9)^{2}

81 cos^{2} (x) - 162 cos (x) cos (9 x) + 81 cos^{2} (9 x)

解答ステップ

(9 cos (x) - cos (9 x) \cdot 9)^{2}

完全平方式を適用する:

(a - b)^{2} = a^{2} - 2 ab + b^{2}

(9 cos (x) - cos (9 x) \cdot 9)^{2} = (9 cos (x))^{2} - 2 \cdot 9 cos (x) cos (9 x) \cdot 9 + (cos (9 x) \cdot 9)^{2}

= (9 cos (x))^{2} - 2 \cdot 9 cos (x) cos (9 x) \cdot 9 + (cos (9 x) \cdot 9)^{2}

簡素化

(9 cos (x))^{2} - 2 \cdot 9 cos (x) cos (9 x) \cdot 9 + (cos (9 x) \cdot 9)^{2} : 81 cos^{2} (x) - 162 cos (x) cos (9 x) + 81 cos^{2} (9 x)

= 81 cos^{2} (x) - 162 cos (x) cos (9 x) + 81 cos^{2} (9 x)