1) 1-3/2sin (x/2+п/3) = 02) ctg (п/3-1/4*х) = 5/12

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31 октября, 15:05

1) 1-3/2sin (x/2+п/3) = 02) ctg (п/3-1/4*х) = 5/12

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Ласточка · Answer 1

1)

1 - 3/2 * sin (x/2 + π/3) = 0;

2 - 3sin (x/2 + π/3) = 0;

3sin (x/2 + π/3) = 2;

sin (x/2 + π/3) = 2/3;

[x/2 + π/3 = arcsin (2/3) + 2πk, k ∈ Z;

[x/2 + π/3 = π - arcsin (2/3) + 2πk, k ∈ Z;

[x/2 = arcsin (2/3) - π/3 + 2πk, k ∈ Z;

[x/2 = π - π/3 - arcsin (2/3) + 2πk, k ∈ Z;

[x/2 = arcsin (2/3) - π/3 + 2πk, k ∈ Z;

[x/2 = 2π/3 - arcsin (2/3) + 2πk, k ∈ Z;

[x = 2arcsin (2/3) - 2π/3 + 4πk, k ∈ Z;

[x = 4π/3 - 2arcsin (2/3) + 4πk, k ∈ Z.

2)

ctg (π/3 - 1/4 * х) = 5/12;

-ctg (x/4 - π/3) = 5/12;

ctg (x/4 - π/3) = - 5/12;

x/4 - π/3 = - arcctg (5/12) + πk, k ∈ Z;

x/4 = π/3 - arcctg (5/12) + πk, k ∈ Z;

x = 4π/3 - 4arcctg (5/12) + 4πk, k ∈ Z.