Срочно!помогите решить:

Question

Срочно!помогите решить:

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Answer 1

Α-β=-π/2⇒α=β-π/2
sin(β-π/2)cosβ=-1/4
-cos²β=-1/4
cos²β=1/4
cosβ=-1/2⇒β=2π/3⇒α=2π/3-π/2=π/6
sin(α+β)=sin(π/6+2π/3)=sin5π/6=1/2
cosβ=1/2⇒β=π/3⇒α=π/3-π/2=-π/6
sin(α+β)=sin(-π/6+π/3)=sinπ/6=1/2