Question

sin^2x+4sinxcosx=5cos^2x

Answer 1

sin^2x+4sinxcosx=5cos^2x
tg^2x+4tgx=5
tg^2x+4tgx-5=0
tgx=1 
tgx=-5
x=π/4+πk
x=-arctg(5)+πk