If tan -1 x - 10 for some x - Rthen the value of -1 x isA- 2 - 5B- - 5C- 4 - 5D- 3 - 5

The correct option is A 2π5 nbsp;We nbsp;know nbsp;thattan 1 nbsp;x nbsp;+ nbsp;cot 1 nbsp;x nbsp;= nbsp;π2, nbsp;x∈R Therefore, nbsp;cot ...

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Properties Derived from Trigonometric Identities

If tan -1 x =...

Question

If ${tan}^{- 1} x = \frac{π}{10} for some x \in R,$
then the value of $c o t^{- 1} x is$

\frac{2 π}{5}

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\frac{π}{5}

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\frac{4 π}{5}

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\frac{3 π}{5}

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\frac{x}{10}

(a) \frac{π}{5} (b) \frac{2 π}{5} (c) \frac{3 π}{5} (d) \frac{4 π}{5}

{tan}^{- 1} x = \frac{π}{10}

x \in R

{cot}^{- 1} x

\tan^{- 1} \frac{x + 1}{x - 1} + \tan^{- 1} \frac{x - 1}{x} = \tan^{- 1}

x

t a n^{- 1} (x - 1) + t a n^{- 1} x + t a n^{- 1} (x + 1) = t a n^{- 1} 3 x

{tan}^{- 1} x = \frac{π}{10} for some x \in R,

c o t^{- 1} x is

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