1) tg x = 1

tg x = 1 = sin x / cos x

sin x = cos x

sin^2 x + cos^2 x = 1

cos^2 x + cos^2 x = 1

2cos^2 x = 1

cos^2 x = 1/2

cos x = ± √(1/2) = ± 1/√2

Для cos x = 1/√2, x = π/4; -3π/4 + 2kπ, где k - целое число

Для cos x = -1/√2, x = 3π/4 + 2kπ; -π/4 + 2kπ, где k - целое число

2) tg x = 1/√3

tg x = 1/√3 = sin x / cos x

sin x = cos x / √3

(1 - cos^2 x) = cos^2 x / 3

3cos^2 x = 3 - cos^2 x

4cos^2 x = 3

cos^2 x = 3/4

cos x = ± √3/2

x = π/6 + kπ, -π/6 + kπ, 5π/6 + kπ, -5π/6 + kπ, где k - целое число

3) ctg x = 1

ctg x = 1 = cos x / sin x

cos x = sin x

cos^2 x + sin^2 x = 1

cos^2 x + cos^2 x = 1

2cos^2 x = 1

cos^2 x = 1/2

cos x = ± √2/2

x = π/4 + kπ, -π/4 + kπ, где k - целое число

4) ctg x = 1/√3

ctg x = 1/√3 = cos x / sin x

cos x = sin x√3

cos^2 x + sin^2 x = 1

cos^2 x + 3sin^2 x = 1

cos^2 x + 3cos^2 x = 1

4cos^2 x = 1

cos^2 x = 1/4

cos x = ± 1/2

x = π/3 + kπ, 5π/3 + kπ, где k - целое число

5) sin x = -0.6

x = arcsin(-0.6) = -0.6435 + 2πk, 2.784 + 2πk

6) cos x = 0.3

x = arccos(0.3) = 1.266 + 2πk, -1.266 + 2πk

Таким образом, решения уравнений найдены.