What is expand (tcos(2t)+sin(t))^2 ?

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

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expand (tcos(2t)+sin(t))^2

expand

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

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

Solution steps

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

Apply Perfect Square Formula:

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

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

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

Simplify

(t cos (2 t))^{2} : t^{2} cos^{2} (2 t)

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

\frac{d}{d t} ((x) 200 (30 - t^{2}))

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

(1 + 2)^{6}

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

(t - b) e^{a t}

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