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

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

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

expand

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

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

Solution steps

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

Apply Perfect Square Formula:

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

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

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

Simplify

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

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

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

(a + b)^{2}

(x - 3)^{2}

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

(1 - cos (θ))^{2}

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