Mathematics - Inverse Trigonometric Functions Question with Solution | TestHub

MathematicsInverse Trigonometric FunctionsMiscellaneous/MixedEasy2 minQB

MathematicsEasysingle choice

If $α$ is the only real root of the equation $x^{3} + b x^{2} + c x + 1 = 0 (b < c)$ then the value of $tan^{- 1} α + tan^{- 1} (\frac{1}{α})$ is

Answer:

Solution:

$f (0) = 1, f (- 1) = b - c < 0 \Rightarrow α \in (- 1, 0) \Rightarrow α < 0$

$∴ tan^{- 1} (α) + tan^{- 1} (\frac{1}{α}) = tan^{- 1} (α) - π + cot^{- 1} α = - π + \frac{π}{2} = - \frac{π}{2}$

Stream:JEESubject:MathematicsTopic:Inverse Trigonometric FunctionsSubtopic:Miscellaneous/Mixed

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