2010-II-46

Ans: B
$\begin{array}{cl}
& \cos^2 1^\circ + \cos^2 2^\circ + \cdots + \cos^2 89^\circ + \cos^2 90^\circ \\
= & (\cos^2 1^\circ + \cos^2 89^\circ) + (\cos^2 2^\circ + \cos^2 88^\circ) + \cdots + (\cos^2 44^\circ + \cos^2 46^\circ) + \cos^2 45^\circ + \cos^2 90^\circ \\
= & (\cos^2 1^\circ + \sin^2 1^\circ) + (\cos^2 2^\circ +\sin^2 2^\circ) + \cdots + (\cos^2 44^\circ + \sin^2 44^\circ) +\cos^2 45^\circ + \cos^2 90^\circ \\
= & 1 \times 44 + (\dfrac{\sqrt{2}}{2})^2 + (0)^2 \\
= & 44.5
\end{array}$