Find the Length of the Curve $r = a \cos ^ { 2 } \left( \frac { \theta } { 2 } \right) , 0 \leq \theta \leq \pi , a > 0$

Multiple Choice

Find the length of the curve.
-The curve $r = a \cos ^ { 2 } \left( \frac { \theta } { 2 } \right) , 0 \leq \theta \leq \pi , a > 0$

A) $\frac { 3 a ^ { 2 } } { 16 }$
B) $\frac { 3 \pi \mathrm { a } ^ { 2 } } { 16 }$
C) $2 a$
D) $2 \pi a$