[tex]4cos^{2}x [/tex]-5sinxcosx+[tex] sin^{2}x [/tex]=0

Разделим на cos²x≠0tg²x-5tgx+4=0tgx=aa²-5a+4=0a1+a2=5 U a1*a2=4a1=1⇒tgx=1⇒x=π/4+πna2=4⇒tgx=4⇒x=arctg4+πn