Question

Пожалуйста,помогите!!$ctgX-tgX-2tg2x-4tg4x+8=0$

Answer 1

ctgx-tgx-2tg2x-4tg4x+8=0;
cosx/sinx- sinx/cosx- 2tg2x-4tg4x +8=0;
(cos²x-sin²x)/(sinx·cosx ) -2sin2x/cos2x -4tg4x +8=0;
2(cos²2x-sin²2x)/(1/2·sin4x) -4sin4x/cos4x +8=0;
4cos4x/sin4x - 4sin4x/cos4x+8=0;
4(cos²4x-sin²4x)/(sin4x·cos4x) +8=0;
8cos8x/sin8x +8=0;
8(ctg8x+1)=0;
ctg8x=-1;⇒
8x=-π/4+kπ;k∈Z;
x=-π/32+kπ/8;k∈Z;