36. dy/dx+2xtan(x-y)=1 then sin(x-y) (1) origin (2) the line x=1/2 (3)The point (1,0) (4) the point (1/2,0)

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t a n^{- 1} \sqrt{(\frac{1 + s i n x}{1 - s i n x})}, \frac{π}{2} < x < π

\frac{d y}{d x}

y = t a n^{- 1} (\frac{\sqrt{1 + sin x} - \sqrt{1 - sin x}}{\sqrt{1 + sin x} + \sqrt{1 - sin x}})

0 < x < \frac{π}{2}

\frac{d y}{d x}

$(2, 0)$ is a point on the line joining the points $(2 x^{2}, 4 x)$ and $(2 y^{2}, 4 y)$ . Then,

y = \frac{sin x}{1 + \frac{cos x}{1 + \frac{sin x}{1 + \frac{cos x}{1 + . . . . . \infty}}}},

\frac{d y}{d x}

x = \frac{π}{2}

y = {cot}^{- 1} [\begin{matrix} \frac{\sqrt{1 + sin x} + \sqrt{1 - sin x}}{\sqrt{1 + sin x} - \sqrt{1 - sin x}} \end{matrix}]

0 < x < \frac{π}{2}

\frac{d y}{d x}

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