3sin²x+sinx*cosx=5cos²x-sin2x
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sin2x=2sinx*cosx
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3sin²x+sinx*cosx-5cos²x+2sinx*cosx=0/cos²x
3tg²x+3tgx-5=0
tgx=a
3a²+3a-5=0
D=9+60=69
a1=(-3-√69)/6⇒tgx=(-3-√69)/3⇒x=-arctg[(3+√69)/6]+πn,n∈z
a2=(-3+√69)/6⇒tgx=(-3+√69)/6⇒x=arctg[(-3+√69)/6]+πk,k∈z