展開する (2cos(t)-tsin(t))^2

解

展開する

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

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

解答ステップ

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

完全平方式を適用する:

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

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

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

簡素化

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

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