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5cosx+2sinx = 3

5cos² (x/2) - 5sin² (x/2) + 4sin (x/2) cos (x/2) - 3sin² (x/2) - 3cos² (x/2) = 0

8sin² (x/2) - 4sin (x/2) cos (x/2) - 2cos² (x/2) = 0 / cos² (x/2) ≠0

8tg² (x/2) - 4tg (x/2) - 2=0

tg (x/2) = a

4a²-2a-1=0

D=4+16=20

a1 = (2-2√5) / 2=1-√5⇒tg (x/2) = 1-√5⇒x/2=arctg (1-√5) + πn⇒x=2arctg (1-√5) + 2πn

a2 = (2+2√5) / 2=1+√5⇒tg (x/2) = 1+√5⇒x/2=arctg (1+√5) + πn⇒2arctg (1+√5) + 2πn