Find the sum of all angles $x \in [0^\circ, 360^\circ]$ that satisfy \[\sin^5 x - \cos^5 x = \frac{1}{\cos x} - \frac{1}{\sin x}.\]
By the way this is what i did, and its wrong, please help still
real solution:
$(-(7 π)/4 + n π)$ in radians
$*180/π$
$-315+180n$
$-315+180n=0$
$n=7/4$
$-315+180n=360$
$n=15/4$
$=1170$
The sum of all x that work is 540 degrees.
