JEE MATHEMATICS MCQ: THEORY OF EQUATION

1 Hard

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Analyzing +4 | -1

{x_1},\;{x_2},\;{x_3},\;{x_4}

are roots of the equation

{x^4} - {x^3}\sin 2\beta + {x^2}\cos 2\beta - xcos\;\beta - \sin \beta = 0

, then

{\tan ^{ - 1}}{x_1} + {\tan ^{ - 1}}{x_2} + {\tan ^{ - 1}}{x_3} + {\tan ^{ - 1}}{x_4}

is equal to

View answer and explanation

Correct option: B

\frac{\pi }{2} - \beta

Option B (

\frac{\pi }{2} - \beta

) is correct because the sum of the arctangents of the roots simplifies to this expression using trigonometric identities and Vieta's formulas.

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