What is expand ((1+cos(2x))/2)^3 ?

The solution to expand ((1+cos(2x))/2)^3 is 1/8+(3cos(2x))/8+(3cos^2(2x))/8+(cos^3(2x))/8

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expand ((1+cos(2x))/2)^3

expand

(\frac{1 + cos ( 2 x )}{2})^{3}

\frac{1}{8} + \frac{3 cos ( 2 x )}{8} + \frac{3 cos ^{2} ( 2 x )}{8} + \frac{cos ^{3} ( 2 x )}{8}

Solution steps

(\frac{1 + cos ( 2 x )}{2})^{3}

Apply exponent rule:

(\frac{a}{b})^{c} = \frac{a ^{c}}{b ^{c}}

= \frac{( 1 + cos ( 2 x ) ) ^{3}}{2 ^{3}}

(1 + cos (2 x))^{3} = 1 + 3 cos (2 x) + 3 cos^{2} (2 x) + cos^{3} (2 x)

= \frac{1 + 3 cos ( 2 x ) + 3 cos ^{2} ( 2 x ) + cos ^{3} ( 2 x )}{2 ^{3}}

2^{3} = 8

= \frac{1 + 3 cos ( 2 x ) + 3 cos ^{2} ( 2 x ) + cos ^{3} ( 2 x )}{8}

Apply the fraction rule:

\frac{a \pm b}{c} = \frac{a}{c} \pm \frac{b}{c}

\frac{1 + 3 cos ( 2 x ) + 3 cos ^{2} ( 2 x ) + cos ^{3} ( 2 x )}{8} = \frac{1}{8} + \frac{3 cos ( 2 x )}{8} + \frac{3 cos ^{2} ( 2 x )}{8} + \frac{cos ^{3} ( 2 x )}{8}

= \frac{1}{8} + \frac{3 cos ( 2 x )}{8} + \frac{3 cos ^{2} ( 2 x )}{8} + \frac{cos ^{3} ( 2 x )}{8}

\frac{( f ( x + h ) - x ^{2} )}{h}

\frac{K ( s + 1 )}{s ( s - 1 ) ( s ^{2} + 10 s + 40 )}

\frac{d}{d y} ((x) (x + y))

\frac{( - w ^{2} - 7 w j - 4 )}{( 2 ( - w ^{2} + 7 w j + 12 ) )}

\frac{2 ( 2 x + 1 )}{5}

What is expand ((1+cos(2x))/2)^3 ?
The solution to expand ((1+cos(2x))/2)^3 is 1/8+(3cos(2x))/8+(3cos^2(2x))/8+(cos^3(2x))/8