What is 1/3 cos^4(t)+sin(t)(sin(t)-(sin^3(t))/3) ?

The solution to 1/3 cos^4(t)+sin(t)(sin(t)-(sin^3(t))/3) is (cos^4(t)+sin(t)(3sin(t)-sin^3(t)))/3

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

simplify

\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}

Solution steps

\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}

Simplify

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}

Join

\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}

\frac{( x + h ) ^{\frac{1}{4}} - x ^{\frac{1}{4}}}{h}

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

(4 - \frac{x ^{2}}{3}) (4 + \frac{x ^{2}}{3})

\frac{( x ^{3} + 6 ) ^{2}}{225}

\frac{8 x ^{2} - 6 x}{( 8 x - 3 ) ^{2}}

What is 1/3 cos^4(t)+sin(t)(sin(t)-(sin^3(t))/3) ?
The solution to 1/3 cos^4(t)+sin(t)(sin(t)-(sin^3(t))/3) is (cos^4(t)+sin(t)(3sin(t)-sin^3(t)))/3