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The value of 2tan^(-1)(cos e ctan^(-1)x-...

The value of `2tan^(-1)(cos e ctan^(-1)x-tancot^(-1)x)` is equal to `cot^(-1)x` (b) `cot^(-1)1/x` `tan^(-1)x` (d) none of these

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`=2 tan^(-1)[cosec(cosec^(-1)frac{sqrt(1+x^2)}{x})-tan(tan^(-1) (1/x))]`
`=2 tan^(-1)[frac{sqrt(1+x^2)-1}{x}]`
`2 tan^(-1)(frac{sec theta -1}{tan theta})`
`2 tan^(-1) atn frac{theta}{2}`
`theta= tan^(-1)x`
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