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

The solution to expand (cos(2t)+2tsin(2t))^2 is cos^2(2t)+4tcos(2t)sin(2t)+4t^2sin^2(2t)

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

expand

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

cos^{2} (2 t) + 4 t cos (2 t) sin (2 t) + 4 t^{2} sin^{2} (2 t)

Solution steps

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

Apply Perfect Square Formula:

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

(cos (2 t) + 2 t sin (2 t))^{2} = cos^{2} (2 t) + 2 cos (2 t) \cdot 2 t sin (2 t) + (2 t sin (2 t))^{2}

= cos^{2} (2 t) + 2 cos (2 t) \cdot 2 t sin (2 t) + (2 t sin (2 t))^{2}

Simplify

cos^{2} (2 t) + 2 cos (2 t) \cdot 2 t sin (2 t) + (2 t sin (2 t))^{2} : cos^{2} (2 t) + 4 t cos (2 t) sin (2 t) + 4 t^{2} sin^{2} (2 t)

= cos^{2} (2 t) + 4 t cos (2 t) sin (2 t) + 4 t^{2} sin^{2} (2 t)

\frac{2 - 2}{3 + 2}

\frac{1}{cos ( x )} \cdot \frac{1}{cos ( x )}

sin^{3} (a) + sin (a) cos^{2} (a)

\frac{x ^{2} - 3 x - 40}{x ^{2} - 8 x}

\frac{2 10}{5}

What is expand (cos(2t)+2tsin(2t))^2 ?
The solution to expand (cos(2t)+2tsin(2t))^2 is cos^2(2t)+4tcos(2t)sin(2t)+4t^2sin^2(2t)