What is expand (1-x^2cos(x))/((1+xsin(x))^2) ?

The solution to expand (1-x^2cos(x))/((1+xsin(x))^2) is (1-x^2cos(x))/(1+2xsin(x)+x^2sin^2(x))

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expand (1-x^2cos(x))/((1+xsin(x))^2)

expand

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

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

Solution steps

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

(1 + x sin (x))^{2} = 1 + 2 x sin (x) + x^{2} sin^{2} (x)

= \frac{1 - x ^{2} cos ( x )}{1 + 2 x sin ( x ) + x ^{2} sin ^{2} ( x )}

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

\frac{s ^{2} - 2 s - 4}{6 ( s ^{3} - 3 s ^{2} - 3 s - 1 )}

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

2 (5 - 4)

\frac{x ^{2} - 4}{x ^{2} + 6 x + 9} \cdot \frac{x - 3}{x ^{3} - 9}

What is expand (1-x^2cos(x))/((1+xsin(x))^2) ?
The solution to expand (1-x^2cos(x))/((1+xsin(x))^2) is (1-x^2cos(x))/(1+2xsin(x)+x^2sin^2(x))