Предмет: Алгебра, автор: liza332

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

Ответы

Автор ответа: daniilgalaev

(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

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