Question

Arccos (-1/2) - arctg (-√3)​

Answer 1

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Answer 2

To calculate the value of the expression Arccos(-1/2) - arctan(-√3), we can use the trigonometric identities and the values of the inverse trigonometric functions.

First, let's find the values of the individual terms:

1. Arccos(-1/2): The cosine function is negative in the second and third quadrants, and the cosine value of -1/2 corresponds to the angle 120 degrees or 2π/3 radians. Therefore, Arccos(-1/2) = 2π/3.

2. Arctan(-√3): The tangent function is negative in the second and fourth quadrants. The tangent value of -√3 corresponds to the angle -60 degrees or -π/3 radians. Therefore, Arctan(-√3) = -π/3.

Now, we can substitute the values back into the original expression:

Arccos(-1/2) - arctan(-√3) = (2π/3) - (-π/3) = 2π/3 + π/3 = π.

Therefore, Arccos(-1/2) - arctan(-√3) is equal to π (pi).