If tan-1 x - -10 for some x - R-then the value of cot-1 x is

nbsp;We nbsp;know nbsp;thattan 1 nbsp;x nbsp;+ nbsp;cot 1 nbsp;x nbsp;= nbsp;π2, nbsp;x∈R Therefore, nbsp;cot 1 nbsp;x nbsp;= nbsp; ...

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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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Solution

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c o t^{- 1} (\frac{1}{x + 1}) + c o t^{- 1} (\frac{1}{x - 1}) =

t a n^{- 1} 3 x - t a n^{- 1} x

x =

{tan}^{- 1} x = \frac{π}{10}

x \in R

{cot}^{- 1} x

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

c o t^{- 1} x is

\frac{x}{10}

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

x

sin [{cot}^{- 1} (1 + x)] = cos ({tan}^{- 1} x)

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