Prove D/dx(sinx)=cosx

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\int \frac{d x}{\sqrt{3} sin x + cos x}

y = \sqrt{cos x + \sqrt{cos x + \sqrt{cos x + . . . . . . . \infty}}}

\frac{d y}{d x} = \frac{- sin x}{(2 y - 1)}

y = \sqrt{sin x + \sqrt{sin x + \sqrt{x} + . . . . \infty}}

\frac{d y}{d x} = \frac{cos x}{2 y - 1}

y = {tan}^{- 1} \frac{sin x}{1 + cos x}

\frac{d y}{d x} = \frac{1}{2}

cos x = \frac{t}{\sqrt{1 + t^{2}}}

sin y = \frac{1}{\sqrt{1 + t^{2}}}

\frac{d y}{d x} = 1

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