2arccos(1/2)+arctg(1)+arsin√2/2

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вопрос

To calculate this expression, we need to use the trigonometric identities and values to find the angles that correspond to the given values.

The value of arccos(1/2) is equal to π/3 because the cosine function equals 1/2 when the angle is π/3.

The value of arctg(1) is equal to π/4 because the tangent function equals 1 when the angle is π/4.

The value of arsin(√2/2) is equal to π/4 because the sine function equals √2/2 when the angle is π/4.

Therefore, the expression simplifies to:

2(π/3) + π/4 + π/4
= 2π/3 + π/2

Therefore, the final answer is 2π/3 + π/2.