展開する (56sin(7t)-33cos(7t))^2

解

展開する

(56 sin (7 t) - 33 cos (7 t))^{2}

3136 sin^{2} (7 t) - 3696 cos (7 t) sin (7 t) + 1089 cos^{2} (7 t)

解答ステップ

(56 sin (7 t) - 33 cos (7 t))^{2}

完全平方式を適用する:

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

(56 sin (7 t) - 33 cos (7 t))^{2} = (56 sin (7 t))^{2} - 2 \cdot 56 sin (7 t) \cdot 33 cos (7 t) + (33 cos (7 t))^{2}

= (56 sin (7 t))^{2} - 2 \cdot 56 sin (7 t) \cdot 33 cos (7 t) + (33 cos (7 t))^{2}

簡素化

(56 sin (7 t))^{2} - 2 \cdot 56 sin (7 t) \cdot 33 cos (7 t) + (33 cos (7 t))^{2} : 3136 sin^{2} (7 t) - 3696 cos (7 t) sin (7 t) + 1089 cos^{2} (7 t)

= 3136 sin^{2} (7 t) - 3696 cos (7 t) sin (7 t) + 1089 cos^{2} (7 t)