cos 2 10° – cos10°cos50° + cos 2 50° = ${1 \over 2}$[ 2cos 2 10° – 2cos10°cos50° + 2cos 2 50°] = ${1 \over 2}$[ 1 + cos20° - cos60° - cos40° + 1 + cos100°] = ${1 \over 2}$[ 2 - ${1 \over 2}$ + cos20° + cos100° - cos40°] = ${1 \over 2}$[ ${3 \over 2}$ + 2cos60°cos40° - cos40°] = ${1 \over 2}$[ ${3 \over 2}$ + cos40° - cos40°] = ${3 \over 4}$