5sin^2 (x) - 5sinxcosx+2cos^2 (x) = 1

5sin²x-5sinxcosx+2cos²x-sin²x-cos²x=0

4sin²x-5sinxcosx+cos²x=0/cos²x

4tg²x-5tgx+1=0

tgx=a

4a²-5a+1=0

D=25-16=9

a1 = (5-3) / 8=1/4⇒tgx=1/4⇒x=arctg1/4+πn, n∈z

a2 = (5+3) / 8=1⇒tgx=1⇒x=π/4+πn, n∈z