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

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

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

simplify

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

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

Solution steps

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

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

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

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

Simplify

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

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

Join

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

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

(1 + x^{2}) \cdot 1 + x^{2}

\frac{8}{3} \cdot (ln (2) - \frac{1}{3})

y^{'} (x) (2 x + 1)^{3}

\frac{1}{48} (x - 5) (x - 3)

(10) \cdot (1 + (12 \cdot 1 0^{- 6} (\circ c)^{- 1})) \cdot (80)

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