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

Question

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

Answer 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