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Find the values of x in (-pi,pi) which s...

Find the values of `x in (-pi,pi)` which satisfy the equation `8^(1+|cosx|+|cos^2x|+|cos^3 x|+........)=4^3`

Text Solution

Verified by Experts

The correct Answer is:
`{+(pi)/(3),pm(2pi)/(3)}`
Given, `2^(1+|cosx|+|cos^(2)x|+|cos^(3)x|+...)=2^(2)`
`implies2^((1)/(1-|cosx|))=2^(2)`
`implies(1)/(1-|cosx|)=2`
`implies|cosx|=(1)/(2)`
`impliescosx=+-(1)/(2)`
`:." "x=(pi)/(3),(2pi)/(3),-(pi)/(3),-(2pi)/(3)" "[becausex in(-pi,pi)]`
Thus, the solution set is `{+-(pi)/(3),+-(2pi)/(3)}.`
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