Trigonometric EquationMedium
Question
If x1, x2, x3, x4 are roots of the equation x4 - x3 sin 2β + x2 cos 2β -x cos β - sin β = 0, then tan-1 x1 + tan-1 x2 + tan-1 x3 + tan-1 x4 =
Options
A.β
B.
- β
- βC.π - β
D.- β
Solution
We have,
∑x1 = sin 2β, ∑x1x2 = cos 2β, ∑x1x2x3 = cos β
and x1x2x3 x4 = - sin β
∴ tan-1
= tan-1 
= tan-1
= tan-1(cot β) = tan
- β
∑x1 = sin 2β, ∑x1x2 = cos 2β, ∑x1x2x3 = cos β
and x1x2x3 x4 = - sin β
∴ tan-1
= tan-1 = tan-1
= tan-1(cot β) = tan - βCreate a free account to view solution
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