Треба розязати:
cos x + sin x/2=0

x={ π+4nπ; (-1)ⁿ⁺¹·π/3+2nπ }, n∈Z

Объяснение:

x/2=t

cos2t+sint=0

1-2sin²t+sint=0

2sin²t-sint-1=0

2sin²t-sint-1=2sin²t-2sint+sint-1=2sint(sint-1)+(sint-1)=(sint-1)(2sint+1)

(sint-1)(2sint+1)=0

1) sint-1=0

sint=1

t=π/2+2nπ

x/2=π/2+2nπ

x=π+4nπ

2) 2sint+1=0

sint=-0,5

t=(-1)ⁿarcsin(-0,5)+nπ

t=(-1)ⁿ⁺¹·π/6+nπ

x/2=(-1)ⁿ⁺¹·π/6+nπ

x=(-1)ⁿ⁺¹·π/3+2nπ