JEE MATHEMATICS MCQ: THEORY OF EQUATION

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Analyzing +4 | -1

\alpha

is only real root of the equation

x^3+\cos 1 \cdot x^2+\sin 1 \cdot x+1=0

, then

\tan ^{-1} \alpha+\tan ^{-1} \frac{1}{\alpha}

is equal to

View answer and explanation

Correct option: C

-\frac{\pi}{2}

Option C (

\frac{-\pi}{2}

) is correct because the real root is negative, and the sum of the arctangents of a number and its reciprocal is

-\frac{\pi}{2}

when the number is negative.

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