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Which of the following is the particular solution to the differential equation: $\cos^2(x)y'=\csc(y)$ given the initial condition $y(0)=\frac{\pi}{2}$ ?

$\tan{x}-\cos(y)=0$

$\tan{x}+\cos(y)=-1$

$\tan{x}-\cos(y)=-1$

$\tan{x}+\cos(y)=0$