簡約 1/3 cos^4(t)+sin(t)(sin(t)-(sin^3(t))/3)

解

簡約

\frac{1}{3} cos^{4} (t) + sin (t) (sin (t) - \frac{sin ^{3} ( t )}{3})

\frac{cos ^{4} ( t ) + sin ( t ) ( 3 sin ( t ) - sin ^{3} ( t ) )}{3}

解答ステップ

\frac{1}{3} cos^{4} (t) + sin (t) (sin (t) - \frac{sin ^{3} ( t )}{3})

\frac{1}{3} cos^{4} (t) = \frac{cos ^{4} ( t )}{3}

sin (t) - \frac{sin ^{3} ( t )}{3} = \frac{3 sin ( t ) - sin ^{3} ( t )}{3}

= \frac{cos ^{4} ( t )}{3} + sin (t) \frac{3 sin ( t ) - sin ^{3} ( t )}{3}

簡素化

sin (t) \frac{3 sin ( t ) - sin ^{3} ( t )}{3} : \frac{sin ( t ) ( 3 sin ( t ) - sin ^{3} ( t ) )}{3}

= \frac{cos ^{4} ( t )}{3} + \frac{sin ( t ) ( 3 sin ( t ) - sin ^{3} ( t ) )}{3}

結合

\frac{cos ^{4} ( t )}{3} + \frac{sin ( t ) ( 3 sin ( t ) - sin ^{3} ( t ) )}{3} : \frac{cos ^{4} ( t ) + sin ( t ) ( 3 sin ( t ) - sin ^{3} ( t ) )}{3}

= \frac{cos ^{4} ( t ) + sin ( t ) ( 3 sin ( t ) - sin ^{3} ( t ) )}{3}