展開する ((cos(t))/t-sin(t)ln(t))^2

解

展開する

(\frac{cos ( t )}{t} - sin (t) ln (t))^{2}

\frac{cos ^{2} ( t )}{t ^{2}} - \frac{sin ( 2 t ) ln ( t )}{t} + sin^{2} (t) ln^{2} (t)

解答ステップ

(\frac{cos ( t )}{t} - sin (t) ln (t))^{2}

完全平方式を適用する:

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

a = \frac{cos ( t )}{t}, b = sin (t) ln (t)

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

簡素化

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

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

簡素化

2 cos (t) sin (t) ln (t) : sin (2 t) ln (t)

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