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

Question

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

Answer 1

(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