Trigonometric EquationHard
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
View Solution FreeMore Trigonometric Equation Questions
Number of values of ′θ′ such that 2 + cos2θ ≥ 3 where θ ∈ [-2π, 2π]...A hyperbola, having the transverse axis of length 2 sinθ, is confocal with the ellipse 3x2 + 4y2 = 12. Then its equ...The maximum distance from origin of a point on the curve x = a sin t - b siny = a cos t - b cos, both a, b > 0 is...If 0o < θ < 180o thenthere being n number of 2′s, is equal to-...If solution of the equation 3cos2θ - 2√3 sin θ cos θ - 3sin2 θ = 0 are nπ + π/r and ...