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