Question

Arcsin π\1+arccos-1+arctg√3+arcctg-√3

Answer 1

Решение задания смотри на фотографии

Answer 2

Let's simplify the expression step by step:

1. Arcsin(π) = π/2 (Arcsin of π is the angle whose sine is π, but since the sine function is limited to the range [-1, 1], Arcsin(π) is not defined. However, in some contexts, it is defined as π/2).

2. Arcsin(1) = π/2 (The arcsine of 1 is π/2 since sin(π/2) = 1).

3. Arccos(-1) = π (The arccosine of -1 is π since cos(π) = -1).

4. Arctg(√3) = π/3 (The arctangent of √3 is π/3 since tan(π/3) = √3).

5. Arcctg(-√3) = 2π/3 (The arccotangent of -√3 is 2π/3 since cot(2π/3) = -√3).

Now, let's plug these values back into the original expression:

π/2 + π - π/3 + 2π/3

Now, let's find a common denominator for the fractions:

The common denominator is 6.

(3π + 6π - 2π + 4π)/6

Combine the terms:

(11π)/6

So, the simplified value of the expression is (11π)/6.