In the range \(0\leq x < 2\pi\) the equation \[2^{\sin^2(x)} + 2^{\cos^2(x)} =2\]

has \(0\) solutions;

has \(1\) solution;

has \(2\) solutions;

holds for all values of \(x\).

In the range \(0\leq x < 2\pi\) the equation \[2^{\sin^2(x)} + 2^{\cos^2(x)} =2\]

has \(0\) solutions;

has \(1\) solution;

has \(2\) solutions;

holds for all values of \(x\).