3sin^ 2x - 0,5sin 4x - 4cos^2 2x= 0

Question

3sin^ 2x - 0,5sin 4x - 4cos^2 2x= 0

Answer 1

3sin²x-sinxcosx-4cos²x=0/cos²x
3tg²x-tgx-4=0
tgx=a
3a²-a-4=0
D=1+48=49
a1=(1-7)/6=-1⇒tgx=-1⇒x=-π/4+πk,k∈z
a2=(1+7)/6=4/3⇒tgx=4/3⇒x=arctg4/3+πn,n∈z