$\frac{\sin \left( \frac{\pi }{2}-x \right)+\cos \left( \frac{\pi }{2}+x \right)}{2\sin \left( \frac{\pi }{2}+x \right)-\cos \left( \frac{\pi }{2}-x \right)}=\frac{\operatorname{cosx}-\operatorname{sinx}}{2\operatorname{cosx}-\operatorname{sinx}}=2$  $\xrightarrow{\operatorname{cosx}\ne 0}\frac{\frac{\operatorname{cosx}}{\operatorname{cosx}}-\frac{\operatorname{sinx}}{\operatorname{cosx}}}{\frac{2\operatorname{cosx}}{\operatorname{cosx}}-\frac{\operatorname{sinx}}{\operatorname{cosx}}}=2\Rightarrow \frac{1-\tan x}{2-\tan x}=2\xrightarrow{\tan x\ne 2}\tan x=3$