$2 t a n^{- 1} (c o s x) = t a n^{- 1} (c o s e c^{2} x)$ ,then x=

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Solution

The correct option is D
$2 t a n^{- 1} (c o s x) = t a n^{- 1} (c o s e c^{2} x) \Rightarrow t a n^{- 1} (\frac{2 c o s x}{1 - c o s^{2} x}) = t a n^{- 1} (\frac{1}{s i n^{2} x}) \Rightarrow \frac{2 c o s x}{s i n^{2} x} = \frac{1}{s i n^{2} x} \Rightarrow 2 c o s x = 1 \Rightarrow x = \frac{π}{3} .$

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