Question

5/cosx-2/sinx=10/sin2x

Answer 1

=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