12 arccos (корень3)|2-3 arccos (-1|2)

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вопрос

We can use the properties of inverse trigonometric functions to simplify these expressions.

arccos(sqrt(3))
Since arccos takes values between 0 and π, we know that arccos(sqrt(3)) = π/6 since cos(π/6) = sqrt(3).

Therefore, 12arccos(sqrt(3)) = 12(π/6) = 2π.

arccos(-1/2)
Since arccos takes values between 0 and π, we know that arccos(-1/2) = 2π/3 since cos(2π/3) = -1/2.

Therefore, 3arccos(-1/2) = 3(2π/3) = 2π.

So, the simplified form of the given expression is 2π.