Алгебра: cos (arcsin(-1/2) -arcsin1)

Question

Алгебра: cos (arcsin(-1/2) -arcsin1)

Answer 1

Arcsin (-1/2) =- π/6,    так как    sin(-π/6)= -1/2    и    -π/6 ∈[ - π/2;π/2]
arcsin 1 =  π/2,      так как    sin(  π/2) = 1    и     π/2 ∈[ - π/2;π/2]

arcsin (-1/2) - arcsin 1 = - π/6 - π/2  = -4π/6=-2π/3

cos(arcsin (-1/2) - arcsin 1) = cos (-2π/3) = cos(2π/3) = - 1/2