Выражение: (cos(5π/2-α)- sin(α-π/(π-α)+cos(3π-α)) - вопрос №40859615238 от amiralimurodov 17.05.2023 07:21

Question

Алгебра: Выражение: (cos(5π/2-α)- sin(α-π/(π-α)+cos(3π-α)) при значении α=-π/8

amiralimurodov · Answer

(cos(5π/2-α)- sin(α-π/2))(sin(π-α)+cos(3π-α))=(cos(2π+π/2-α)+sin(π/2-α))(sin(π-α)+cos(2π+π-α))=(cos(π/2-α)+sin(π/2-α))(sin(π-α)+cos(π-α))=(sinα+cosα)(sinα-cosα)=sin²α-cos²α=-(cos²-sin²α)=-cos2α=-cos(-π/8×2)=-cos(π/4)=-√2/2...