What is expand ((1+cos(2x))/2)((1+cos(2x))/2) ?

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

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expand ((1+cos(2x))/2)((1+cos(2x))/2)

expand

(\frac{1 + cos ( 2 x )}{2}) (\frac{1 + cos ( 2 x )}{2})

cos^{4} (x)

Solution steps

(\frac{1 + cos ( 2 x )}{2}) (\frac{1 + cos ( 2 x )}{2})

Remove parentheses:

(a) = a

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

Multiply fractions:

\frac{a}{b} \cdot \frac{c}{d} = \frac{a \cdot c}{b \cdot d}

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

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

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

Multiply the numbers:

2 \cdot 2 = 4

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

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

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

Rewrite using trig identities

= cos^{4} (x)

, (\frac{2}{3} x + \frac{2}{3}) (\frac{4 y}{3} + \frac{1}{3})

(\frac{16 - a}{2})^{2}

(a \cdot b^{'} + c) (a + b)

\frac{3}{2} (y = 1)^{2} - 3 y (y + 1)

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