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

Evaluate

\frac{4 sin ^{3} ( x ) cos ^{3} ( x )}{( sin ^{4} ( x ) cos ^{4} ( x ) ) ^{2}}

Multiply the terms

\frac{4 sin ^{3} ( x ) cos ^{3} ( x )}{( ( sin ( x ) cos ( x ) ) ^{4} ) ^{2}}

Evaluate the power

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\frac{4 sin ^{3} ( x ) cos ^{3} ( x )}{( sin ( x ) cos ( x ) ) ^{8}}

Factor the expression

\frac{4 sin ^{3} ( x ) cos ^{3} ( x )}{sin ^{8} ( x ) cos ^{8} ( x )}

Reduce the fraction

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\frac{4 cos ^{3} ( x )}{sin ^{5} ( x ) cos ^{8} ( x )}

Reduce the fraction

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\frac{4}{sin ^{5} ( x ) cos ^{5} ( x )}

Multiply the terms

\frac{4}{( sin ( x ) cos ( x ) ) ^{5}}

Transform the expression

\frac{4}{( \frac{s i n ( 2 x )}{2} ) ^{5}}

Rewrite the expression

\frac{4}{\frac{s i n ^{5} ( 2 x )}{32}}

Multiply by the reciprocal

4 \times \frac{32}{sin ^{5} ( 2 x )}

Multiply the terms

\frac{4 \times 32}{sin ^{5} ( 2 x )}

Multiply the terms

\frac{128}{sin ^{5} ( 2 x )}

Solution

128 csc^{5} (2 x)

Simplify the expression