Алгебра. Решите пожалуйста ) X*x^lgx=10x 2sinx*cos^2x-sinx-sin^2x=0

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

sin(x)*(2cos(x) - 1 - sin(x)) = 0

sin(x)*(cos(2x) - sin(x)) = 0

sin(x) = 0 --> x = πk

1 - 2sin(x) - sin(x) = 0

sin(x) = -1 --> x = -π/2 + 2πk

sin(x) = 1/2 --> x = (-1)ᵏ*π/6 + πk

Ответ: πk, -π/2 + 2πk, (-1)ᵏ*π/6 + πk, k - целое.