Note that i made it (+) sinx/cosx because otherwise, it won't be equal. Double check if your plus/minus signs are correct :)
[tex] \frac{sinx}{sinx} + \frac{cosx}{sinx} - \frac{cosx}{cosx} + \frac{sinx}{cosx} = secxcscx[/tex]
[tex]1+ \frac{cosx}{sinx} - 1 + \frac{sinx}{cosx} = \frac{1}{cosx}}\frac{1}{sinx}[/tex]
[tex] \frac{cos^2x + sin^2 x}{cosxsinx} = \frac{1}{cosxsinx}[/tex]
[tex]\frac{1}{cosxsinx} = \frac{1}{cosxsinx}[/tex]