Question

надо доказать тождество 

Answer 1

$(sin alpha +cos alpha ) ^{2}+(sin alpha -cos alpha ) ^{2}= \ =si n ^{2} alpha +2cdot sin alpha cdot cos alpha+cos ^{2} alpha +sin ^{2} alpha -2cdot sin alpha cdot cos alpha +cos ^{2} alpha = \ =2(sin ^{2} alpha +cos ^{2} alpha )=2cdot1=2$