Решите 6sinx^2-4sin2x=-1

Question

Решите 6sinx^2-4sin2x=-1

Answer 1

6sin²x-8sinxcosx+sin²x+cos²x=0/cos²x
7tg²x-8tgx+1=0
tgx=a
7a²-8a+1=0
D=64-28=36
a1=(8-6)/14=1/7⇒tgx=1/7⇒x=arctg1/7+πn,n∈z
a2=(8+6)/14=1⇒tgx=1⇒x=π/4+πk,k∈z