Prove the following trigonometrical identities: \[ \frac{1+\tan x}{\sin x}+\frac{1+\cot x}{\cos ...

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Prove the following trigonometrical identities:
\[
\frac{1+\tan x}{\sin x}+\frac{1+\cot x}{\cos x}=2(\sec x+\operatorname{cosec} x)
\]
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