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

We know that tan^ 1x+^ 1x=π2 ^ 1x=π2 π10 =5π π10 =4π10 =2π5 ...

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Domain and Range of Basic Inverse Trigonometric Functions

If tan-1x=π...

Question

If ${tan}^{- 1} x = \frac{π}{10}$ for some $x \in R$ , then find the value of ${cot}^{- 1} x$ .

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{sin}^{- 1} x = \frac{π}{5}

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{cos}^{- 1} x .

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

{tan}^{- 1} \frac{x - 1}{x - 2} + {tan}^{- 1} \frac{x + 1}{x + 2} = \frac{π}{4}

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x < 0, {tan}^{- 1} x + {tan}^{- 1} \frac{1}{x} = \frac{π}{2}

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If $s i n^{- 1} x = \frac{π}{5}$ for some $x ϵ (- 1, 1),$ then the value of $c o s^{- 1} x$ is
[IIT 1992]

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