展開する (tcos(t)+2sin(t))^2

解

展開する

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

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

解答ステップ

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

完全平方式を適用する:

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

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

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

簡素化

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

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