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|4 Videos

  • TRIGONOMETRIC FUNCTIONS

    CENGAGE|Exercise SINGLE CORRECT ANSWER TYPE|38 Videos

Similar Questions

Explore conceptually related problems

The number of solution (s) of the equation sqrt2+cos 2 x=(sin x+cos x) in [-pi/2, pi]

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

The number of solutions of the equation |2 sin x-sqrt(3)|^(2 cos^(2) x-3 cos x+1)=1 in [0, pi] is

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

Number of solutions of the equation sin x + cos x-2sqrt(2) sin x cos x=0 for x in [0, pi] is

Number of solutions of the equation 4(cos^(2) 2x+ cos 2 x +1)+tan x (tan x-2sqrt(3))=0 in [0, 2pi] is

The number of distinct of real roots of the equation tan^(2)2x+2tan2x tan3x-1=0 in the interval [0,(pi)/(2)] is

The number of solutions of the equation 3^(2sec^(2)x)+1=10.3^(tan^(2)x) in the interval [0,2pi] is

The number of solutions of the equation x^3 +2 x^2 +5 x + 2 cos x = 0 in (0,2 pi] is

The number of solutions of the equation cos^(2)((pi)/(3)cos x - (8pi)/(3))=1 in the interval [0,10pi] is