展開する sqrt(144t^2+(9cos^2(t)+9cos(t)sin(t))^2)

解

展開する

144 t^{2} + (9 cos^{2} (t) + 9 cos (t) sin (t))^{2}

3 16 t^{2} + 9 cos^{4} (t) + 18 cos^{3} (t) sin (t) + 9 cos^{2} (t) sin^{2} (t)

解答ステップ

144 t^{2} + (9 cos^{2} (t) + 9 cos (t) sin (t))^{2}

拡張

144 t^{2} + (9 cos^{2} (t) + 9 cos (t) sin (t))^{2} : 144 t^{2} + 81 cos^{4} (t) + 162 cos^{3} (t) sin (t) + 81 cos^{2} (t) sin^{2} (t)

= 144 t^{2} + 81 cos^{4} (t) + 162 cos^{3} (t) sin (t) + 81 cos^{2} (t) sin^{2} (t)

因数

144 t^{2} + 81 cos^{4} (t) + 162 cos^{3} (t) sin (t) + 81 cos^{2} (t) sin^{2} (t) : 9 (16 t^{2} + 9 cos^{4} (t) + 18 cos^{3} (t) sin (t) + 9 cos^{2} (t) sin^{2} (t))

= 9 (16 t^{2} + 9 cos^{4} (t) + 18 cos^{3} (t) sin (t) + 9 cos^{2} (t) sin^{2} (t))

累乗根の規則を適用する:

n ab = n a n b,

, 以下を想定

a \geq 0, b \geq 0

= 9 16 t^{2} + 9 cos^{4} (t) + 18 cos^{3} (t) sin (t) + 9 cos^{2} (t) sin^{2} (t)

9 = 3

= 3 16 t^{2} + 9 cos^{4} (t) + 18 cos^{3} (t) sin (t) + 9 cos^{2} (t) sin^{2} (t)