展開する ((1-cos(6x))^2)/4

解

展開する

\frac{( 1 - cos ( 6 x ) ) ^{2}}{4}

\frac{1}{4} - \frac{cos ( 6 x )}{2} + \frac{cos ^{2} ( 6 x )}{4}

解答ステップ

\frac{( 1 - cos ( 6 x ) ) ^{2}}{4}

(1 - cos (6 x))^{2} = 1 - 2 cos (6 x) + cos^{2} (6 x)

= \frac{1 - 2 cos ( 6 x ) + cos ^{2} ( 6 x )}{4}

分数の規則を適用する:

\frac{a \pm b}{c} = \frac{a}{c} \pm \frac{b}{c}

\frac{1 - 2 cos ( 6 x ) + cos ^{2} ( 6 x )}{4} = \frac{1}{4} - \frac{2 cos ( 6 x )}{4} + \frac{cos ^{2} ( 6 x )}{4}

= \frac{1}{4} - \frac{2 cos ( 6 x )}{4} + \frac{cos ^{2} ( 6 x )}{4}

キャンセル

\frac{2 cos ( 6 x )}{4} : \frac{cos ( 6 x )}{2}

= \frac{1}{4} - \frac{cos ( 6 x )}{2} + \frac{cos ^{2} ( 6 x )}{4}