Question

Cos^2(18°)+cos^2(36°)+cos^2(54°)+cos^2(72°)

Answer 1

answer:

${ \cos }^{2} (18) + { \cos }^{2} (36) + { \cos }^{2}(54) + { \cos }^{2} \: (72 ) \\ { \cos }^{2} (90 - 72) + { \cos}^{2} (90 - 54) + { \cos }^{2} (54)+ { \cos}^{2} (72) \\ { \sin }^{2}(72) + { \sin }^{2} (54) + { \cos}^{2} (54) + { \cos}^{2} (72) \\ ({ \sin}^{2} (72) + { \cos}^{2} (72) )+ ( { \sin }^{2}( 54) + { \cos }^{2} (54)) \\ = 1 + 1 \\ = 2$