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Verified answer

5sin2x+5cosx-8sinx-4=0
10sinxcosx+5cosx-8sinx-4=0
5cosx(2sinx+1)-4(2sinx+1)=0
(5cosx-4)(2sinx+1)=0
1) 5cosx=4
cosx=4/5
x=arccos4/5+2Пn

2) 2sinx=-1
sinx=-1/2
x=-П/6+2Пn
x=-5П/6+2Пn