Answer
$y-π/4=\frac{1}{2}(x-π/2)$
or
$y=\frac{1}{2}x$
Work Step by Step
Take the derivative of both sides of the equation. Remember to apply chain rule:
$2ycos2x+sin2x\times dy/dx=-2xsiny\times dy/dx+cos2y$
Solve for dy/dx:
$dy/dx(sin2x+2xsiny)=cos2y-2ycos2x$
$dy/dx=\frac{cos2y-2ycos2x}{sin2x+2xsiny}$
Plug in the point (π/2, π/4) into dy/dx to solve for the slope:
$dy/dx=\frac{-π/2\times (-1)+0}{0+π\times 1}=\frac{π/2}{π}=\frac{1}{2}$
Plug in the point and slope into point slope form:
$y-π/4=\frac{1}{2}(x-π/2)$
or
$y=\frac{1}{2}x$
