5/cosx-2/sinx=10/sin2x
=5/cosx - 2/sinx = 10/2sinxcosx
5/cosx - 2/sinx - 5/sinxcosx = 0
(5sinx-2cosx-5)/cosxsinx = 0
5sinx - 2cosx = 5
5*2t/(1+t^2) - 2* (1-t^2)/(1+t^2)=5
t1= 7/3 tg(x/2)=7/3 x=2arctg(7/3)+2pk
t2= 1 tg(x/2)=1 x=p/2 +2pk (не удовл.)
Ответ: x=2arctg(7/3)+2pk