Question

cos^2 2x-3sin 2x*cos2x=-1
Решите пожалуйста

Answer 1

cos²2x-3sin2xcos2x=-1;⇒
cos²2x-3sin2xcos2x+cos²2x+sin²2x=0;⇒
2cos²2x+sin²2x-3sin2xcos2x=0;⇒делим на cos²2x;cos²2x≠0;
2+tg²2x-3tg2x=0;⇒tg2x=t;⇒
t²-3t+2=0;
t₁,₂=3/2⁺₋√9/4-2=3/2⁺₋1/2;
t₁=2;⇒tg2x=2;2x=arctg2+kπ;k∈Z;x=1/2arctg2+kπ/2;k∈Z;
t₂=1;⇒tg2x=1;2x=π/4+kπ;k∈Z;x=π/8+kπ/2;k∈Z;