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

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

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

expand

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

cos^{4} (x)

Solution steps

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

Apply exponent rule:

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

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

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

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

2^{2} = 4

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

Rewrite using trig identities

= cos^{4} (x)

- 2 a (- 2 a e^{- a x^{2}} x^{2} + e^{- a x^{2}})

(e^{u} + e^{- u})^{2}

(2 - 1 1)

d (1 - cos (u))

\frac{6 c ^{2}}{5 d ^{3} ( t ^{2} - 8 t ^{3} ) ^{6}}

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