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

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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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