Решите уравнение:

5/cosx=5tgx+4cosx

5/cosx=5sinx/cosx+4cosx

cosx≠0

5=5sinx+4cos²x

5-5sinx-4+4sin²x=0

sinx=a

4a²-5a+1=0

D=25-16=9

a1 = (5-3) / 8=1/4⇒sinx=1/4⇒x = (-1) ^n*arcsin1/4+πn, n∈z

a2 = (5+3) / 8=1⇒sinx=1⇒x=π/2+2πn, n∈z