Find co$s^2$5° + co$s^2$10° + co$s^2$15° + … + co$s^2$85°.

There are 17 terms. Pair co$s^2$$k$° with co$s^2(90-k)$° = si$n^2$$k$°: eight pairs (5° with 85°, …, 40° with 50°) give 8, and co$s^2$45° = 1/2 is left over. Total 8 1/2.