Question

cos3x/(sin3x-2sinx)=tgx

Answer 1

cos(3x)/(sin(3x) - 2sin(x)) = tg(x)
(4cos³(x) - 3cos(x))/(3sin(x) - 4sin³(x) - 2sin(x)) = tg(x)
(cos(x)*(4cos²(x) - 3)/(sin(x)*(1 - 4sin²(x))) = tg(x)
cos(x)*(2cos(2x) - 1)/(sin(x)*(2cos(2x) - 1) = tg(x)
ctg(x) = tg(x) --> tg(x) = ±1 --> x = π/4 + πk/2, k - целое.