Решите уравнение

ctgxcos5x = cos 6x + sin5x

Сosxcos5x/sinx=cos6x+sin5x

sinx≠0

cosxcos5x-cos6xsinx-sin5xsimx=0

(cosxcos5x-sinxsin5x) - cos6xsinx=0

cos (5x+x) - cos6xsinx=0

cos6x * (1-sinx) = 0

cos6x=0⇒6x=π/2+πn⇒x=π/12+πn/6, n∈z

sinx=1⇒x=π/2+2πk, k∈z