If $$x1$$,$$x2$$,$$x3$$,$$x4are$$ roots of the equation $$x4$$−$$x3sin2$$β$$+x2cos2$$β−xcosβ−$$sin$$β$$=0then$$ Tan−$$1x1+Tan$$−$$1x2+Tan$$−$$1x3+Tan$$−$$1x4=$$

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If  $$x1$$,$$x2$$,$$x3$$,$$x4are$$ roots of the equation $$x4$$−$$x3sin2$$β$$+x2cos2$$β−xcosβ−$$sin$$β$$=0then$$ Tan−$$1x1+Tan$$−$$1x2+Tan$$−$$1x3+Tan$$−$$1x4=$$

Infinity Learn · Accepted Answer

from the given equation∑$$x1=sin2$$β;∑$$x1x2=cos2$$β;∑$$x1x2x3=$$$$cos$$β;and $$x1x2x3x4=$$−$$sin$$β∴$$tan$$−$$1(x1)+$$$$tan$$−$$1x2+$$$$tan$$−$$1x3+$$$$tan$$−$$1x4=$$$$tan$$−$$1$$∑$$x1$$−∑$$x1x2x31$$−∑$$x1x2+x1x2x3x4=$$$$tan$$−$$1sin2$$β$$-$$$$cos$$β$$1-cos2$$β$$-$$$$sin$$β$$=$$$$tan$$−$$12sin$$β$$cos$$β$$-$$$$cos$$β$$2sin2$$β$$-$$$$sin$$β$$=$$$$tan$$−$$1cos$$β$$2sin$$β$$-1sin$$β$$2sin$$β$$-1=$$$$tan$$−$$1cot$$β$$=$$$$tan$$−$$1tan$$$$π$$$$2-$$β$$=$$π$$2-$$β

If $x_{1}, x_{2}, x_{3}, x_{4}$ are roots of the equation $x^{4} - x^{3} \sin 2 β + x^{2} \cos 2 β - x \cos β - \sin β = 0$ then ${Tan}^{- 1} x_{1} + {Tan}^{- 1} x_{2} + {Tan}^{- 1} x_{3} + {Tan}^{- 1} x_{4} =$

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If x1,x2,x3,x4are roots of the equation x4−x3sin2β+x2cos2β−xcosβ−sinβ=0then Tan−1x1+Tan−1x2+Tan−1x3+Tan−1x4=

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If $x_{1}, x_{2}, x_{3}, x_{4}$ are roots of the equation $x^{4} - x^{3} \sin 2 β + x^{2} \cos 2 β - x \cos β - \sin β = 0$ then ${Tan}^{- 1} x_{1} + {Tan}^{- 1} x_{2} + {Tan}^{- 1} x_{3} + {Tan}^{- 1} x_{4} =$