展開する (2sin(x)+2cos(x))^2

解

展開する

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

4 sin (2 x) + 4

解答ステップ

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

完全平方式を適用する:

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

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

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

簡素化

(2 sin (x))^{2} + 2 \cdot 2 sin (x) \cdot 2 cos (x) + (2 cos (x))^{2} : 4 (sin (2 x) + 1)

= 4 (sin (2 x) + 1)

分配法則を適用する:

a (b + c) = ab + a c

4 (sin (2 x) + 1) = 4 sin (2 x) + 4 \cdot 1

= 4 sin (2 x) + 4 \cdot 1

数を乗じる:

4 \cdot 1 = 4

= 4 sin (2 x) + 4