(sin alpha+cos alpha)²=2-(sin alpha-cos alpha)² доказать - вопрос №64353002 от bobrikov01 26.11.2021 12:47

Question

Алгебра: (sin alpha+cos alpha)²=2-(sin alpha-cos alpha)² доказать тождество.

bobrikov01 · Answer

(sinα+cosα)²=2-(sinα-cosα)1. (sinα+cosα)²=sin²α+2sinα*cosα+cos²α==(sin²α+cos²α)+2sinα*cosα=1+2sinα*cosα2. 2-(sinα-cosα)²=2-(sin²α-2sinα*cosα+cos²α)=2-(sin²α+cos²α-2sinα*cosα)==2-(1-2sinα*cosα)=2-1-(-2sinα*cosα)=1+2sinα*cosα3. 1+2sinα*cosα=1+2sinα*cosα ч. т. д....