$$\tan \alpha+2 \tan 2 \alpha+4 \tan 4 \alpha+8 \cot 8 \alpha$$ is equal to

If $$f(x)=\frac{\cot x}{1+\cot x}$$ and $$\alpha+\beta=\frac{5 \pi}{4}$$, then the value of $$f(\alpha) f(\beta)$$ is equal to

In $$\triangle A B C \cdot \frac{a+b+c}{B C+A B}+\frac{a+b+c}{A C+A B}=3$$, then $$\tan \frac{C}{8}$$ is equal to

Mean of the values $$\sin ^2 10 Y, \sin ^2 20 Y, \sin ^2 30 Y, \ldots \ldots \ldots ., \sin ^2 90 Y$$ is