Решить sin(x+1)=sinx+sin1

Question

Решить
sin(x+1)=sinx+sin1

Answer 1

Sin(x+1) =sinx+sin1;
2sin(x+1)/2* cos(x+1)/2 =2sin(x+1)/2*cos(x-1)/2 ;
sin(x+1)/2 (cos(x+1)/2 - cos(x-1)/2) =0 ;
-2sin(x+1)/2*sin(x/2)*sin1/2 =0 ;
-2sin1/2 ≠ 0 ;
[sin(x+1)/2 = 0 ; sin(x/2) = 0.
[(x+1)/2 = πk ; x/2 = πk.
[x = 2πk -1  ; x =2 πk , k∈Z.