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## Homework Statement

find arc length of the segment of the 2space curbe that is defined by the parametric equations

x(t) = t-sin(t)

y(t) = 1+cos(t)

0 ≤ t ≤ 4π

## The Attempt at a Solution

I've found dx/dt and dy/dt respectively and put them into the arc length equation, i.e. sqrt[(dx/dt)²+(dy/dt)²]

dx/dt = 1-cost

dy/dt = -sint

therefore arc length L = sqrt[(1-cost)²+(-sint)²]

this leads to L = sqrt[1-2cost+cos²t+sin²t]

I am then told to use the double angle formula 2sin²t = 1-cos2t to simplify the integrand. I cannot see how this applies though!

If someone could point me in the right direction