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

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giorgiana1976 | College Teacher | (Level 3) Valedictorian

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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

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