2(sinx+cosx)=ctgx+1
Help!!!!!!

Ответ:

x1 = -pi/4 + pi*n; n ∈ Z; x2 = pi/6 + 2pi*k; k ∈ Z; x3 = 5pi/6 + 2pi*k; k ∈ Z

Объяснение:

2(sin x + cos x) = cos x/sin x + sin x/sin x

2(sin x + cos x) = (cos x + sin x)/sin x

2(sin x + cos x) - (cos x + sin x)/sin x = 0

(sin x + cos x)(2 - 1/sin x) = 0

1) sin x + cos x = 0

Делим все на cos x ≠ 0

sin x/cos x + 1 = 0

tg x = -1

x1 = -pi/4 + pi*n; n ∈ Z

2) 2 = 1/sin x

sin x = 1/2

x2 = pi/6 + 2pi*k; k ∈ Z

x3 = 5pi/6 + 2pi*k; k ∈ Z