If \( y=e^{\tan x} \), prove that \( \left(\cos ^{2} x\right) \frac{d^{2} y}{d x^{2}}-(1+\sin 2 ...

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If \( y=e^{\tan x} \), prove that \( \left(\cos ^{2} x\right) \frac{d^{2} y}{d x^{2}}-(1+\sin 2 x) \cdot \frac{d y}{d x}=0 \)
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