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

\frac{3 π}{4}

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\frac{π}{4}

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\frac{π}{3}

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None of these

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Solution

The correct option is B $\frac{π}{4}$
We have $2 t a n^{- 1} (c o s x) = t a n^{- 1} (2 c o s e c x)$
$\Rightarrow t a n^{- 1} (\frac{2 c o s x}{1 - c o s^{2} x}) = t a n^{- 1} (2 c o s e c x)$
$\frac{2 c o s x}{s i n^{2} x} = 2 c o s e c x \Rightarrow 2 c o s x = 2 s i n x$
or $s i n x = c o s x$
$\Rightarrow x = \frac{π}{4}$ .

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