+195 Use the double-angle formula for cosine: cos 2α = 2cos^2 α - 1.
Rewrite each cos^2 term using the double-angle formula: cos^2 1 = (cos 2 * 1 + 1) / 2, cos^2 2 = (cos 2 * 2 + 1) / 2, ..., cos^2 89 = (cos 2 * 89 + 1) / 2.
Substitute the new expressions into the original sum: (cos 2 * 1 + 1) / 2 + (cos 2 * 2 + 1) / 2 + ... + (cos 2 * 89 + 1) / 2.
Notice that the terms with "cos 2 * α" cancel out in pairs due to the periodic nature of the cosine function.
The sum simplifies to 44 / 2 = 22.
