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Find the sum of all angles $x \in [0^\circ, 360^\circ]$ that satisfy $\sin^5 x - \cos^5 x = \frac{1}{\cos x} - \frac{1}{\sin x}.$

Jul 8, 2021

#1
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real solution:

$(-(7 π)/4 + n π)$ in radians

$*180/π$

$-315+180n$

$-315+180n=0$

$n=7/4$

$-315+180n=360$

$n=15/4$

$=1170$

Jul 8, 2021
#2
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The sum of all x that work is 540 degrees.

Jul 9, 2021