展開する (4cos(t)-sin(t))^2

解

展開する

(4 cos (t) - sin (t))^{2}

16 cos^{2} (t) - 8 cos (t) sin (t) + sin^{2} (t)

解答ステップ

(4 cos (t) - sin (t))^{2}

完全平方式を適用する:

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

(4 cos (t) - sin (t))^{2} = (4 cos (t))^{2} - 2 \cdot 4 cos (t) sin (t) + sin^{2} (t)

= (4 cos (t))^{2} - 2 \cdot 4 cos (t) sin (t) + sin^{2} (t)

簡素化

(4 cos (t))^{2} - 2 \cdot 4 cos (t) sin (t) + sin^{2} (t) : 16 cos^{2} (t) - 8 cos (t) sin (t) + sin^{2} (t)

= 16 cos^{2} (t) - 8 cos (t) sin (t) + sin^{2} (t)