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

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

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expand (cos(x)-xsin(x))^2

expand

(cos (x) - x sin (x))^{2}

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

Solution steps

(cos (x) - x sin (x))^{2}

Apply Perfect Square Formula:

(a - b)^{2} = a^{2} - 2 ab + b^{2}

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

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

Simplify

cos^{2} (x) - 2 cos (x) x sin (x) + (x sin (x))^{2} : x^{2} sin^{2} (x) - x sin (2 x) + cos^{2} (x)

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

(x + y) (x + y)

\frac{2 x - 12}{( x - 4 ) ( x - 5 )}

(a - x)^{4}

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

25 (6 + 2)

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