$$ \sin \alpha+\cos \alpha=m \Rightarrow \sin ^6 \alpha+\cos ^6 \alpha= $$

If $\sin A=\frac{-7}{25}, \cos B=\frac{8}{17}, A$ does not lie in the 3rd quadrant and $B$ does not lie in the 1st quadrant, then $8 \tan A-5 \cot B=$

If $\sin \theta-\cos \theta=\frac{1}{\sqrt{3}}$, then $\sin (2 \theta)+\cos (4 \theta)+\sin (6 \theta)=$

If $a \tan \alpha+b \tan \beta=(a+b) \tan \left(\frac{\alpha+\beta}{2}\right)$ and $\alpha-\beta \neq 2 n \pi$ then $\frac{\cos \beta}{\cos \alpha}=$