What is expand 1/4 (1-cos(x))^2 ?

The solution to expand 1/4 (1-cos(x))^2 is (1+cos^2(x))/4-(cos(x))/2

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expand 1/4 (1-cos(x))^2

expand

\frac{1}{4} (1 - cos (x))^{2}

\frac{1 + cos ^{2} ( x )}{4} - \frac{cos ( x )}{2}

Solution steps

\frac{1}{4} (1 - cos (x))^{2}

Expand

(1 - cos (x))^{2} : 1 - 2 cos (x) + cos^{2} (x)

= \frac{1}{4} (1 - 2 cos (x) + cos^{2} (x))

Apply the distributive law:

m (a + b + c) = ma + mb + m c

\frac{1}{4} (1 - 2 cos (x) + cos^{2} (x)) = \frac{1}{4} \cdot 1 + \frac{1}{4} (- 2 cos (x)) + \frac{1}{4} cos^{2} (x)

= \frac{1}{4} \cdot 1 + \frac{1}{4} (- 2 cos (x)) + \frac{1}{4} cos^{2} (x)

Simplify

\frac{1}{4} \cdot 1 + \frac{1}{4} (- 2 cos (x)) + \frac{1}{4} cos^{2} (x) : \frac{1 + cos ^{2} ( x )}{4} - \frac{cos ( x )}{2}

= \frac{1 + cos ^{2} ( x )}{4} - \frac{cos ( x )}{2}

1 - cos (x) + ln (2) (1 + tan (22 x)) + 2 arcsin (3 x)

\frac{e ^{2} π}{π ^{2} + 1} cos (π (t - 2))

(1 + cos (4 x))^{2}

2 (1 + 2 x) sin (1 + 2 x) + 2 (1 - 2 x) sin (1 - 2 x)

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

What is expand 1/4 (1-cos(x))^2 ?
The solution to expand 1/4 (1-cos(x))^2 is (1+cos^2(x))/4-(cos(x))/2