Question

CosX+sinY=0.5 cosX-sinY=0.5

Answer 1

Если уравнения системы сложить, то останется только cosx, если их  вычесть - останется  только  siny.
2cosx=1
2siny=0.
cosx=1/2, x= +-π/3 +2πn, n∈Z.
siny=0, y=πk,k∈Z.
 ответ: x= +-π/3 +2πn, n∈Z, y=πk,k∈Z.

Answer 2

To solve this system of equations:

CosX + sinY = 0.5 ... (1)

cosX - sinY = 0.5 ... (2)

We can add equations (1) and (2) to get:

2 cosX = 1

So, cosX = 1/2

Substituting cosX = 1/2 in equation (1):

1/2 + sinY = 0.5

sinY = 0

So, Y = nπ where n is any integer.

Thus, the solutions to the system of equations are:

X = π/3 + 2nπ, Y = nπ where n is any integer.