Let's break down the given expression step by step:
arcsin(-1) = -π/2Since sin(-π/2) = -1
arcsin(1/2) = π/6Since sin(π/6) = 1/2
Therefore, arcsin(-1) + arcsin(1/2) = -π/2 + π/6 = -3π/6 + π/6 = -2π/6 = -π/3
So, Ctg(arcsin(-1) + arcsin(1/2)) = Ctg(-π/3) = Ctg(-60°) = -√3
Let's break down the given expression step by step:
arcsin(-1) = -π/2
Since sin(-π/2) = -1
arcsin(1/2) = π/6
Since sin(π/6) = 1/2
Therefore, arcsin(-1) + arcsin(1/2) = -π/2 + π/6 = -3π/6 + π/6 = -2π/6 = -π/3
So, Ctg(arcsin(-1) + arcsin(1/2)) = Ctg(-π/3) = Ctg(-60°) = -√3