If f ( x )= tan x +2 tan 2 x +3 tan 3 x +4 tan 4 x + ldots ldots ∞ where x ∈((-π/4), (π/4)) ∪((3 π/4), (5 π/4)), then number of solution(s) of the equation f(x)=2, is(are)

Question

If f ( x )= tan x +2 tan 2 x +3 tan 3 x +4 tan 4 x + ldots ldots ∞ where x ∈((-π/4), (π/4)) ∪((3 π/4), (5 π/4)), then number of solution(s) of the equation f(x)=2, is(are) (A) 1 (B) 2 (C) 3 (D) 4

Tardigrade Admin · Accepted Answer

f ( x )=( tan x /(1- tan x )2)=2 ⇒ 2 tan 2 x -5 tan x +2=0 ⇒ tan x =(1/2), 2 text (rejected) ∴ Number of solutions are 2 .

Q. If $f (x) = tan x + 2 tan^{2} x + 3 tan^{3} x + 4 tan^{4} x + \dots\dots \infty$ where $x \in (\frac{- π}{4}, \frac{π}{4}) \cup (\frac{3 π}{4}, \frac{5 π}{4})$ , then number of solution(s) of the equation $f (x) = 2$ , is(are)

1

2

3

4

$f (x) = \frac{t a n x}{( 1 - t a n x ) ^{2}} = 2$
$\Rightarrow 2 tan^{2} x - 5 tan x + 2 = 0$
$\Rightarrow tan x = \frac{1}{2}, 2 (rejected)$
$∴$ Number of solutions are 2 .

Q. If f(x)=tanx+2tan2x+3tan3x+4tan4x+……∞ where x∈(4−π​,4π​)∪(43π​,45π​), then number of solution(s) of the equation f(x)=2, is(are)

1

2

3

4

f(x)=(1−tanx)2tanx​=2 ⇒2tan2x−5tanx+2=0 ⇒tanx=21​,2 (rejected) ∴ Number of solutions are 2 .

Q. If $f (x) = tan x + 2 tan^{2} x + 3 tan^{3} x + 4 tan^{4} x + \dots\dots \infty$ where $x \in (\frac{- π}{4}, \frac{π}{4}) \cup (\frac{3 π}{4}, \frac{5 π}{4})$ , then number of solution(s) of the equation $f (x) = 2$ , is(are)

$f (x) = \frac{t a n x}{( 1 - t a n x ) ^{2}} = 2$
$\Rightarrow 2 tan^{2} x - 5 tan x + 2 = 0$
$\Rightarrow tan x = \frac{1}{2}, 2 (rejected)$
$∴$ Number of solutions are 2 .