3sin^2x + cos^2x = 2sin2x

Question

3sin^2x + cos^2x = 2sin2x

Answer 1

3sin²x+cos²x-4sinxcosx=0/cos²x
3tg²x-4tgx+1=0
tgx=a
3a²-4a+1=0
D=16-12=4
a1=(4-2)/6=1/3⇒tgx=1/3⇒x=arctg1/3+πn,n∈z
a2=(4+2)/6=1⇒tgx=1⇒x=π/4+πk,k∈z