Determine the tangent to the curve y = sin^2(x)/x at the point, x = pi/2. Leave your answer in the form ax+by+c=0

First determine the y coordinate of the curve at the given x coordinate, in this case, y = sin²(pi/2)/(pi/2) = 1²/(pi/2) = 2/piDifferentiate the function with respect to x to determine the gradient of the tangent at the point, this expression requires the quotient rule.u = sin²(x) u' = 2sin(x)cos(x) = sin(2x) (by chain rule)v = x v' = 1Quotient rule: y' = (vu' - uv')/v²y' = (xsin(2x) - sin²(x))/x²At the point x = pi/2y' = (pi/2 (sin(pi) - sin²(pi/2))/(pi/2)² = 0 - 4/pi² = -4/pi²Equation of a line (y-y₁) = m(x-x₁)y-2/pi = -4/pi²(x-pi/2)Rearranging this gives the tangent to be 4x + (pi²)y - 4pi = 0