Question

Сделайте пожалуйста ...б) arccos(-1/2)-2arcsin√3/2+arctg1-3arcctg1; в) cos п/10*cos 2п/5+sin п/10*sin 2п/5; очень надо ..

Answer 1

Б) = 5π/6 -2*π/3 + π/4 - 3*π/4= -π/3
в) = Cos(π/10 - 2π/5) = Cos (-3π/10)= Cos0,3π

Answer 2

Calculation of the Expression

To calculate the given expression, let's break it down step by step.

a) arccos(-1/2) - 2arcsin(√3/2) + arctg(1) - 3arcctg(1)

1. arccos(-1/2): - The arccos function returns the angle whose cosine is the given value. - arccos(-1/2) is equal to 2π/3 or 120 degrees [[1]].

2. 2arcsin(√3/2): - The arcsin function returns the angle whose sine is the given value. - arcsin(√3/2) is equal to π/3 or 60 degrees [[2]]. - Multiplying it by 2 gives 2π/3 or 120 degrees.

3. arctg(1): - The arctg function returns the angle whose tangent is the given value. - arctg(1) is equal to π/4 or 45 degrees [[3]].

4. 3arcctg(1): - The arcctg function returns the angle whose cotangent is the given value. - arcctg(1) is equal to π/4 or 45 degrees [[4]]. - Multiplying it by 3 gives 3π/4 or 135 degrees.

Now, let's substitute the values we obtained into the expression:

arccos(-1/2) - 2arcsin(√3/2) + arctg(1) - 3arcctg(1) = 2π/3 - 2π/3 + π/4 - 3π/4

Simplifying the expression:

2π/3 - 2π/3 + π/4 - 3π/4 = 0 + π/4 - 3π/4 = -2π/4 = -π/2

Therefore, the value of the expression arccos(-1/2) - 2arcsin(√3/2) + arctg(1) - 3arcctg(1) is -π/2.

b) cos(π/10) * cos(2π/5) + sin(π/10) * sin(2π/5)

To calculate this expression, we can use the trigonometric identity:

cos(a - b) = cos(a) * cos(b) + sin(a) * sin(b)

Using this identity, we can rewrite the expression as:

cos(π/10) * cos(2π/5) + sin(π/10) * sin(2π/5) = cos(π/10 - 2π/5)

Simplifying the expression inside the cosine function:

π/10 - 2π/5 = π/10 - 4π/10 = -3π/10

Therefore, the value of the expression cos(π/10) * cos(2π/5) + sin(π/10) * sin(2π/5) is cos(-3π/10).

Please note that the exact value of cos(-3π/10) cannot be determined without further simplification or approximation.

If you have any further questions, feel free to ask!