What is expand (x^2)/((cos(x)+xsin(x))^2) ?

The solution to expand (x^2)/((cos(x)+xsin(x))^2) is (x^2)/(cos^2(x)+xsin(2x)+x^2sin^2(x))

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expand (x^2)/((cos(x)+xsin(x))^2)

expand

\frac{x ^{2}}{( cos ( x ) + x sin ( x ) ) ^{2}}

\frac{x ^{2}}{cos ^{2} ( x ) + x sin ( 2 x ) + x ^{2} sin ^{2} ( x )}

Solution steps

\frac{x ^{2}}{( cos ( x ) + x sin ( x ) ) ^{2}}

(cos (x) + x sin (x))^{2} = cos^{2} (x) + x sin (2 x) + x^{2} sin^{2} (x)

= \frac{x ^{2}}{cos ^{2} ( x ) + x sin ( 2 x ) + x ^{2} sin ^{2} ( x )}

\frac{10 x ^{2} + 50 x}{( 2 x + 5 ) ^{2}}

1.3 (1 + e^{0, 4 \cdot \frac{3}{7}})

\frac{( x + 3 )}{( x ^{2} + 2 x + 2 ) ( x ^{3} + 10 x ^{2} + 29 x + 20 )}

\frac{5 + 4 x - 3 x ^{2}}{( 1 - 2 x ) ( 2 + x ) ^{2}}

\frac{5 s + e ^{- 3 s}}{s ^{2} ( s ^{2} + 1 )} + 5 s

What is expand (x^2)/((cos(x)+xsin(x))^2) ?
The solution to expand (x^2)/((cos(x)+xsin(x))^2) is (x^2)/(cos^2(x)+xsin(2x)+x^2sin^2(x))