Solve the system of equations six*cosy=0.25 and siny*cosx=0.75 .

Adding the 1st equation to the 2nd one, we'll
get:

sin x*cos y + sin y*cos x =
0.25+0.75

sin x*cos y + sin y*cos x =
1

We'll recognize the
formula:

sin (x+y) = 1

x + y =
pi/2 + k*pi (3)

Subtracting the 1st equation from the 2nd
one, we'll get:

sin y*cos x - sin x*cos y = 0.75 -
0.25

sin y*cos x - sin x*cos y =
0.50

We'll recognize the
formula:

sin (y-x) = 0.50 =
1/2

y - x = (-1)^k*pi/6 + k*pi
(4)

We'll add (3) to (4):

2y =
pi/2 + (-1)^k*pi/6 + 2k*pi

y = pi/4 +
(-1)^k*pi/12 + k*pi

x = pi/2 + k*pi - pi/4 -
(-1)^k*pi/12 - k*pi

x = pi/4 -
(-1)^k*pi/12