Question

Используя тождество $sing ^{2} \alpha +cos ^{2} \alpha =1$, упростите выражения:
$(sin \alpha +cos \alpha ) ^{2} +(sin \alpha -cos \alpha ) ^{2} =$
$sin ^{4} \alpha +2sin ^{2} \alpha *cos ^{2} \alpha +cos ^{4} \alpha =$
$cos ^{2} \alpha -cos ^{4} \alpha +sin ^{4} \alpha =$

Answer 1

(sina+cosa)²+(sina-cosa)²=sin²a+2sina*cosa+cos²a+sin²a-2sina*cosa+cos²a=
=2(sin²a+cos²a)=2*1=2
sin^4a+2sin²a*cos²a+cos^4a=(sin²a+cos²a)²=1²=1
cos²a-cos^4+sin^4=cos²a-(cos^4a-sin^4a)=cos²a-(cos²a-sin²a)(cos²a+sin²a)=
=cos²a-(cos²a-sin²a)*1=cos²a-cos²a+sin²a=sin²a