If $$(1+\tan 1^{\circ})(1+\tan 2^{\circ}) \ldots(1+\tan 45^{\circ})=2^n,$$ then $$n=$$

$$\frac{\cos \theta}{1-\tan \theta}+\frac{\sin \theta}{1-\cot \theta}=$$

If $$\operatorname{cosech} x=\frac{4}{5}$$, then $$\sinh x=$$

What is the value of $$\cos \left(22 \frac{1}{2}\right)^{\circ}$$ ?