Home
Class 12
MATHS
Find the number of roots of the equation...

Find the number of roots of the equation `tan(x+pi/6)=2tanx ,forx in (0,3pi)dot`

Text Solution

Verified by Experts

`tan (x+pi/6)=2tan x`
`rArr (tan x +"tan" pi/6)/(1- tan x "tan" pi/6)=2 tan x`
Let `tan x=y`.
`rArr (y+1/sqrt(3))/(1- y/sqrt(3))=2y`
`rArr (sqrt(3) y+1)/(sqrt(3)-y)=2y`
`rArr sqrt(3) y+1=2sqrt(3) y-2y^(2)`
`rArr 2y^(2)-sqrt(3)y+1=0`, which has imaginary roots.
Hence, equation has no solutions.
Promotional Banner

Topper's Solved these Questions

  • TRIGONOMETRIC EQUATIONS

    CENGAGE|Exercise Exercise 4.1|12 Videos

  • TRIGONOMETRIC EQUATIONS

    CENGAGE|Exercise Exercise 4.2|6 Videos

  • TRIGNOMETRIC RATIOS IDENTITIES AND TRIGNOMETRIC EQUATIONS

    CENGAGE|Exercise Question Bank|4 Videos

  • TRIGONOMETRIC FUNCTIONS

    CENGAGE|Exercise SINGLE CORRECT ANSWER TYPE|38 Videos

Similar Questions

Explore conceptually related problems

Find the number of solutions of the equation 3tanx+x^3=2in(0,pi/4)

Find the number of solution to the equation x^(2)tanx=1,x in [0,2pi].

Find the number of solution of the equation cot^(2) (sin x+3)=1 in [0, 3pi] .

Find the number of solution of the equation x^(3)+2x+cosx+tanx=0 in (-(pi)/(2),(pi)/(2))

The number of roots of the equation sin(2x+pi/18) cos(2x-pi/9)=-1/4 in [0, 2pi] is

Find the number of solution of the equation sqrt(cos 2x+2)=(sin x + cos x) in [0, pi] .

The number of roots of the equation xsinx=1,x in [-2pi,0)uu(0,2pi] is 2 (b) 3 (c) 4 (d) 0

The number of solutions of equations |tan2x|=sin x" in"[0,pi]

The number of solutions of the equation cos^2(x+pi/6)+cos^2x-2cos(x+pi/6)dotcospi/6=sin^2pi/6 in interval ((-pi)/2,pi/2) is_________

the number of solution of the equation tanx + sec x = 2 cos x and cos x ne 0 lying in the interval ( 0 , 2 pi ) is