Let `Ssub(0,pi)` denote the set of values of `x` satisfying the equation `8^1+|cos x|+cos^2x+|cos^(3x| tooo)=4^3` . Then, `S=` `{pi//3}` b. `{pi//3,""2pi//3}` c. `{-pi//3,""2pi//3}` d. `{pi//3,""2pi//3}`

Options

A. `{pi//3}`
B. `{pi//6,5pi//6}`
C. `{pi//3,5pi//6}`
D. `{pi//3,2pi//3}`

Answer

D

Explanation

We know that
`-1lecosle1`
`rArrabs(cosx)le1`
But, `xinSrArrxin(0,pi)rArrabs(cosx)lt1`
Now,
`8^(1+abs(cosx)+cos^(2)x+abs(cos^(3)x)+..."to"oo)=4^(3)`
`rArr8^(1//(1-abs(cosx)))=8^(2)`
or `1/(1-abs(cosx))=2`
or `abs(cosx)=1/2`
or cos x=`pm1/2`
or `x=pi/3,2pi/3`
`rArrS={pi//3,2pi//3}`