6cos 2x-14sinxcosx -14cos^2 x=0

Question

6cos 2x-14sinxcosx -14cos^2 x=0

Comments

уравнение

Answer 1

6cos²x-6sin²x-14sinxcosx-14cos²x=0/cos²x
6tg²x+14tgx+8=0
tgx=a
6a²+14a+8=0
D=196-192=4
a1=(-14-2)/12=-4/3⇒tgx=-4/3⇒x=-arctg4/3+πn,n∈z
a2=(-14+2)/12=-1⇒tgx=-1⇒x=-π/4+πk,k∈z