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

The solution to (1/2+1/2 cos(2x))^4 is cos^8(x)

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simplify (1/2+1/2 cos(2x))^4

simplify

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

cos^{8} (x)

Solution steps

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

Simplify

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

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

Apply exponent rule:

(a^{b})^{c} = a^{b c},

assuming

a \geq 0

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

Multiply the numbers:

2 \cdot 4 = 8

= cos^{8} (x)

(x - x y) d y

e^{x} (x + 2)

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

(csc (θ) - 1) (sin (θ) + 1)

(D - 3) (e^{3 x} y)