Упрастите выражение: sin(α-β)-sin(п/2-α)sin(-β)

Question

Упрастите выражение: sin(α-β)-sin(п/2-α)sin(-β)

Answer 1

1 вариант sin(alpha-beta)-sin(пи/2-alpha)*sin(-beta)

sin(alpha)*cos(beta)

(sin(beta+alpha)-sin(beta-alpha))/2 

2 вариант sin(alpha-beta)-sin(пи/(2-alpha))*sin(-beta)

(-cos(alpha)-sin(пи/(alpha-2)))*sin(beta)+sin(alpha)*cos(beta)

sin(alpha)*cos(beta)-(cos(alpha)+sin(пи/(alpha-2)))*sin(beta)

sin(alpha)*cos(beta)-(cos(alpha)+sin(пи/(alpha-2)))*sin(beta)

(cos(alpha*beta/(alpha-2)-2*beta/(alpha-2)+пи/(alpha-2))-cos(alpha*beta/(alpha-2)-2*beta/(alpha-2)-пи/(alpha-2))-2*sin(beta-alpha))/2