Question

Розвяжіть рівняння 1) cos(x-π/9)=-1 2) 2sin(2x-π/3)=√2/2 3)ctg x/2=√3

Answer 1

1) Решение:
cos9x=-1
9x=π+2πn
x=π/9+2πn/9

2.)
x\2=arcctg(-koren z 3)+pn, nє z
x=2*5p\6+pn, n є z
x=5p\3+pn, n є z

Answer 2

1) cos(x-π/9) = -1 To solve this equation, we need to find the values of x that satisfy the given equation. We know that the cosine function has a period of 2π, so we can add 2π to the angle inside the cosine function without changing its value. So, we can write the equation as: cos(x-π/9) = cos(π)

Now, we know that the cosine function is equal to 1 when the angle inside it is 0, and it is equal to -1 when the angle inside it is π. So, we have: x-π/9 = π x = π + π/9 x = π(1 + 1/9) x = π(10/9)

So, the solution to the equation is: x =