Does this:$(\cos x) ^{\frac{1}{\cos x}}+(\sin x) ^{\frac{1}{\sin x}}=1$ have integers solution?

Question

I want to know if this equation $(\cos x) ^{\frac{1}{\cos x}}+(\sin x) ^{\frac{1}{\sin x}}=1$ have integers solution , however wolfram alpha assumed all it solutions are real , but probably there is any method to disproof or proof that is has solutions in integers ?