Question

The value of x in \[(-\pi,\pi)\] which satisfies the equation \[\large 8^{(1+ \left|cosx \right|+\left|\cos^{2}x \right|+\left|\cos^{3}x \right|+.......\infty )}=4^{3}\] is ???

Answer 1

ques. from series and sequences.

Answer 2

8*8 = 4^3

Answer 3

is that power??

Answer 4

if that is power, then
then the value of summation is 2
|cos x| <= 1, since this has to converge < 1
we know for G.S.
1/(1 - |cos x|) = 2
1 - |cos x| = 1/2 => x = pi/6 or 5pi/6

Answer 5

sorry pi/3 and 2pi/3 ... 60 and 120