MathematicsIf x = a (cost + t sin t), y = a (sin t – t cos t) then dxdt2+dydt2 =

If x = a (cost + t sin t), y = a (sin t - t cos t) then $\sqrt{{[\frac{d x}{d t}]}^{2} + {[\frac{d y}{d t}]}^{2}}$ =

The given equations are x = a (cost + t sin t), y = a (sin t - t cos t)

Differentiate both functions with respect to the parameter $t$ $\frac{d x}{d t} = a (- \sin t + t \cos t + \sin t) = a t \cos t$

$\frac{d y}{d t} = a (\cos t - \cos t + t \sin t) = a t \sin t$

Therefore, $\sqrt{{(\frac{d y}{d t})}^{2} + {(\frac{d x}{d t})}^{2}} = a t (1) = a t$

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