Find the most general solution of `2^1|cosx|+cos^2x+|cosx|^(3+oo)=4` – InterviewSolution

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1.	Find the most general solution of `2^1\|cosx\|+cos^2x+\|cosx\|^(3+oo)=4`
Answer» We have `2^(1+\|cos x\|+cos^(2)x+\|cos x\|^(3)+...oo)=4` or `2^(1+\|cos x\|+\|cos x\|^(2)+\|cos x\|^(3)+...oo)=4` or `2^(1/(1-\|cos x\|))=2^(2)` (sum of infinite G.P.) or `1/(1-\|cos x\|)=2` or `\|cos x\|=1/2 or cos x = pm 1/2` `rArr x=n pi pm pi/3, n in Z`

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