Решите уравнение 3cos(x+1)-4sin(x+1)=5

Question

Решите уравнение
3cos(x+1)-4sin(x+1)=5

Answer 1

X+1=t
3cos²t/2-3sin²t/2-8sint/2cost/2-5sin²t/2-5cos²t/2=0
-8sin²t/2-8sint/2cost/2-2cos²t/2=0/(-2cos²t/2)
4tg²t/2+4tgt/2+1=0
(2tgt/2+1)²=0
2tgt/2=-1
tgt/2=-1/2
t/2=-arctg1/2+πn,n∈z
t=-2arctg1/2+2πn∈z
x+1=-2arctg1/2+2πn∈z
x=-1-2arctg1/2+2πn∈z