12cosx - 5 sinx = -6, 5

12cosx - 5sinx = -6,5
Введём дополнительный угол С:
C = 12 + 5 = 13
Разделим на 13:
cosx12/13 - 5/13sinx = -1/2
cosxcos(arccos(12/13)) - 5sin(arccos(12/13)sinx = -1/2
cos(x + arccos(12/13)) = -1/2
x + arccos(12/13)  = 2/3 + 2n, n  Z
x = 2/3 - arccos(12/13) + 2n, n  Z

Cosx=(1-tgx/2))/(1+tgx/2),sinx=2tgx/2/(1+tgx/2)
tgx/2=ucosx=(1-u)/(1+u) ,sinx=2u/(1+u)
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12cosx-5sinx=-13/2
24cosx-10sinx=-13
24*(1-u)/(1+u)-10*2u/(1+u)=-13
24(1-u)-20u=-13(1+u)=0
24-24u-20u+13+13u=0
11u-20u-37=0
D=400+1628=2028
D=263
u1=(20-263)/22=(10-133)/11 U u2=(10+133)/11
tgx/2=(10-133)/11x/2=arctg[(10-133)/11]+k
x=2arctg[(10-133)/11]+k,kz
tgx/2=(10+133)/11x/2=arctg[(10+133)/11]+k
x=2arctg[(10+133)/11]+k,kz