Question

Решите уравнения:
sin 2x + cos x = 0
(cos 2x - 1) tg x = 0

Answer 1

sin2x+cosx = 0;
2sinx*cosx +cosx =0;
2cosx*(sinx +1/2) =0;
cosx=0 ⇒x=π/2 +2π*k , k∈Z;
sinx+1/2=0 ;
sinx =-1/2;
x= (-1)^(k+1) +π*k.
==========================
(cos2x-1)tqx=0;  
ОДЗ:   x ≠ π/2 +π*k;
{cos2x-1=0  и   tqx  существует    cos2x=1⇒2x =2π*k ⇔x=π*k; 
tqx=0 ⇒  x=π*k