展開する (-3sin(x)+3sin(3x))^2+(3cos(x)-cos(3x)*3)^2

解

展開する

(- 3 sin (x) + 3 sin (3 x))^{2} + (3 cos (x) - cos (3 x) \cdot 3)^{2}

36 sin^{2} (x)

解答ステップ

(- 3 sin (x) + 3 sin (3 x))^{2} + (3 cos (x) - cos (3 x) \cdot 3)^{2}

拡張

(- 3 sin (x) + 3 sin (3 x))^{2} : 9 sin^{2} (x) - 18 sin (x) sin (3 x) + 9 sin^{2} (3 x)

= 9 sin^{2} (x) - 18 sin (x) sin (3 x) + 9 sin^{2} (3 x) + (3 cos (x) - cos (3 x) \cdot 3)^{2}

拡張

(3 cos (x) - cos (3 x) \cdot 3)^{2} : 9 cos^{2} (x) - 18 cos (x) cos (3 x) + 9 cos^{2} (3 x)

= 9 sin^{2} (x) - 18 sin (x) sin (3 x) + 9 sin^{2} (3 x) + 9 cos^{2} (x) - 18 cos (x) cos (3 x) + 9 cos^{2} (3 x)

簡素化

9 sin^{2} (x) - 18 sin (x) sin (3 x) + 9 sin^{2} (3 x) + 9 cos^{2} (x) - 18 cos (x) cos (3 x) + 9 cos^{2} (3 x) : 36 sin^{2} (x)

= 36 sin^{2} (x)