Home
Class 12
MATHS
Let S={xepsilon(-pi,pi):x!=0,+pi/2}The s...

Let `S={xepsilon(-pi,pi):x!=0,+pi/2}`The sum of all distinct solutions of the equation `sqrt3secx+cosecx+2(tan x-cot x)=0` in the set S is equal to

A

`-(7 pi)/9`

B

`-(2pi)/9`

C

0

D

`(5pi)/9`

Text Solution

Verified by Experts

The correct Answer is:
C
`sqrt(3) sec x + cosec x =2 (cot x - tan x)`
`rArr sqrt(3)/(cos x)+1/(sin x) =2 ((cos x)/(sin x)-(sin x)/(cos x))`
`rArr sqrt(3) sin x + cos x =2(cos^(2) x-sin^(2) x)`
`rArr cos (x-pi/3)=cos 2x`
`rArr 2x= 2npi pm (x-pi/3), n in Z`
`rArr x=2n pi - pi/3, (2 n pi)/3 +pi/9`
In `(-pi, pi), x = (-pi)/3, pi/9, (7pi)/9, (-5pi)/9`
`:. Sigmax_(i)=0`
Promotional Banner

Topper's Solved these Questions

  • TRIGONOMETRIC EQUATIONS

    CENGAGE|Exercise Archives (Matrix Match Type)|1 Videos

  • TRIGONOMETRIC EQUATIONS

    CENGAGE|Exercise JEE Main Previous Year|2 Videos

  • TRIGNOMETRIC RATIOS IDENTITIES AND TRIGNOMETRIC EQUATIONS

    CENGAGE|Exercise Question Bank|34 Videos

  • TRIGONOMETRIC FUNCTIONS

    CENGAGE|Exercise SINGLE CORRECT ANSWER TYPE|38 Videos

Similar Questions

Explore conceptually related problems

Let S={x varepsilon(-pi,pi):x!=0,+(pi)/(2)} The sum of all distinct solutions of the equation root(3)(3)sec x+cos ecx+2(tan x-cot x)=0 in the set S is equal to

The sum of all the solutions in [0, 4pi] of the equation tan x+ cot x+1= cos (x+pi/4) is

The number of solutions of the equation tan x+secx=2 cos x lying in the interval [0, 5pi] is

If the sum of all the solutions of the equation 8cos x*(cos((pi)/(6)+x)cos((pi)/(6)-x)-(1)/(2))=1 in [0,pi] is k pi then k is equal to