What is expand (cos(t)-tsin(t))^2 ?

The solution to expand (cos(t)-tsin(t))^2 is t^2sin^2(t)-tsin(2t)+cos^2(t)

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expand (cos(t)-tsin(t))^2

expand

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

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

Solution steps

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

Apply Perfect Square Formula:

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

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

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

Simplify

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

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

(1 - x)^{2}

(x - 3)^{2}

(x + i y)^{4}

(1 + tan (x))^{2}

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

What is expand (cos(t)-tsin(t))^2 ?
The solution to expand (cos(t)-tsin(t))^2 is t^2sin^2(t)-tsin(2t)+cos^2(t)