(xsina-ucosa)^2+(xcosa+ysina)^2=x^2 +y^2

u = x tan(A) - sec(A) sqrt(x^2 + y^2 - (x cos(A) + y sin(A))^2) or u = sec(A) sqrt(x^2 + y^2 - (x cos(A) + y sin(A))^2) + x tan(A)

Step-by-step explanation:

Solve for u:

(x sin(A) - u cos(A))^2 + (x cos(A) + y sin(A))^2 = x^2 + y^2

Subtract (x cos(A) + y sin(A))^2 from both sides:

(x sin(A) - u cos(A))^2 = x^2 + y^2 - (x cos(A) + y sin(A))^2

Take the square root of both sides:

x sin(A) - u cos(A) = sqrt(x^2 + y^2 - (x cos(A) + y sin(A))^2) or x sin(A) - u cos(A) = -sqrt(x^2 + y^2 - (x cos(A) + y sin(A))^2)

Subtract x sin(A) from both sides:

-u cos(A) = sqrt(x^2 + y^2 - (x cos(A) + y sin(A))^2) - x sin(A) or x sin(A) - u cos(A) = -sqrt(x^2 + y^2 - (x cos(A) + y sin(A))^2)

Divide both sides by -cos(A):

u = x tan(A) - sec(A) sqrt(x^2 + y^2 - (x cos(A) + y sin(A))^2) or x sin(A) - u cos(A) = -sqrt(x^2 + y^2 - (x cos(A) + y sin(A))^2)

Subtract x sin(A) from both sides:

u = x tan(A) - sec(A) sqrt(x^2 + y^2 - (x cos(A) + y sin(A))^2) or -u cos(A) = -x sin(A) - sqrt(x^2 + y^2 - (x cos(A) + y sin(A))^2)

Divide both sides by -cos(A):

 u = x tan(A) - sec(A) sqrt(x^2 + y^2 - (x cos(A) + y sin(A))^2) or u = sec(A) sqrt(x^2 + y^2 - (x cos(A) + y sin(A))^2) + x tan(A)

1 + (6 / x - 1)

step-by-step explanation:

divide using polynomial division.