展開する (e^{tcos(x)}(t)-e^{tsin(x)}(t))^2

解

展開する

(e^{t c o s (x)} (t) - e^{t s i n (x)} (t))^{2}

e^{2 t c o s (x)} t^{2} - 2 e^{t c o s (x) + t s i n (x)} t^{2} + e^{2 t s i n (x)} t^{2}

解答ステップ

(e^{t c o s (x)} (t) - e^{t s i n (x)} (t))^{2}

括弧を削除する:

(a) = a

= (e^{t c o s (x)} t - e^{t s i n (x)} t)^{2}

完全平方式を適用する:

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

a = e^{t c o s (x)} t, b = e^{t s i n (x)} t

= (e^{t c o s (x)} t)^{2} - 2 e^{t c o s (x)} t e^{t s i n (x)} t + (e^{t s i n (x)} t)^{2}

簡素化

(e^{t c o s (x)} t)^{2} - 2 e^{t c o s (x)} t e^{t s i n (x)} t + (e^{t s i n (x)} t)^{2} : e^{2 t c o s (x)} t^{2} - 2 e^{t c o s (x) + t s i n (x)} t^{2} + e^{2 t s i n (x)} t^{2}

= e^{2 t c o s (x)} t^{2} - 2 e^{t c o s (x) + t s i n (x)} t^{2} + e^{2 t s i n (x)} t^{2}