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Popular >

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

Solution

simplify

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

Solution

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}}

Simplify

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

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

2^{2} = 4

= \frac{4 cos ^{4} ( x )}{4}

Divide the numbers:

\frac{4}{4} = 1

= cos^{4} (x)

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Frequently Asked Questions (FAQ)

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