Home
Class 12
MATHS
If the sum of all the solutions of the e...

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

A

`20//9`

B

`2//3`

C

`13//9`

D

`8//9`

Text Solution

Verified by Experts

The correct Answer is:
C
`8 cos x (cos (pi/6+x) cos (pi/6-x)-1/2)=1`
`rArr 8 cos x [cos^(2) pi/6- sin^(2) x-1/2]=1`
`rArr 8 cos x [1/4-(1-cos^(2) x)]=1`
`rArr 8cos^(3)x-6 cos x =1`
`rArr 4 cos^(3) x-3 cos x=1/2`
`rArr cos 3 x=1/2="cos" pi/3`
`3x=2npi pm pi/3, n in Z`
Since `x in [0, pi]`, possible values are
`3x=pi/3, 2pi pm pi/3`
`:. x=pi/9, (5pi)/9, (7pi)/9`
sum of solution `=(13 pi)/9`
`:. k=13/9`
Promotional Banner

Topper's Solved these Questions

  • TRIGONOMETRIC EQUATIONS

    CENGAGE|Exercise JEE Advanced Previous Year|10 Videos

  • TRIGONOMETRIC EQUATIONS

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

  • TRIGONOMETRIC EQUATIONS

    CENGAGE|Exercise Exercise (Numerical)|21 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 solutions of the equation |2 sin x-sqrt(3)|^(2 cos^(2) x-3 cos x+1)=1 in [0, pi] is

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

The sum of all the solution of the equation costhetacos(pi/3+theta)cos(pi/3-theta)=1/4theta in [0,6pi] (A) 15pi (B) 30pi (C) (100pi)/3 (D) none of these

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

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

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

The number of solutions of equation cos2x-3cos x+1=(1)/((cot2x-cotx).sin(x-pi)) in [0,4pi] is

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

The number of solution of the equation |cos x|=cos x-2 sin x "in"[0,6 pi] is

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