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//3,-2pi//3]`
C. `[-pi//3,-2pi//3]`
D. `[pi//3,2pi//3]`

Answer

D

Explanation

We know that
`-1lecosxle1rArr|cosx|le1`.
But, `x inSrArrx in(0,pi)rArr|cos^(3)x|+ . . ."to "oo=4^(3)`
`rArr" "8^(1//1-|cosx|)=8^(2)`
`rArr" "(1)/(1-|cosx|)=2`
`rArr" "|cosx|=(1)/(2)`
`rArr" "cosx=pm(1)/(2)rArrx=pi//3,2pi//3rArrS={pi//3,2pi//23}`