#25 and 26 pls#
astral chasmBOT
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formal pebble
$\textbf{26.}$ one may rewrite the sum as $\sum_{i=0}^{\infty}\abs{\cos x}^i$ and since $0<x<\pi$ we know that $\abs{\cos x}<1$ thus the geometric series is convergent
rustic ventureBOT
#EqualityForWolf
formal pebble
i assume that this is what the problem statement means, by "inscribed in an angle alpha". please confirm.
sharp lake
aren’t there supposedly two values of x for question 26?
vernal sandal
No
formal pebble
**\#EqualityForWolf**
@vernal sandal are you able to solve it with this
formal pebble
aren’t there supposedly two values of x for question 26?
only one of them lies in (0,pi)
the expression is $4^{\frac{1}{1-\abs{\cos x}}}$
rustic ventureBOT
#EqualityForWolf
sharp lake
only one of them lies in (0,pi)
shouldn't x and π-x end up having the same value after all the absolute value signs?
formal pebble
shouldn't x and π-x end up having the same value after all the absolute value si...
ah
yes you're right
which gives two solutions in (0,pi)