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
Let L be the line of intersection of the planes 2x + 3y + z = 1 and x + 3y + 2z = 2. If L makes an angles α with th...Match List-I with List-II and select the correct answer using the code given below the lists....The most general values of x for which sin x + cos x = {1, a2 − 4a + 6} are given by -...Which one is not periodic...If sin θ = and θ lies in the second quadrant then sec θ + tan θ =...