If $2 \tan ^{-1} x=3 \sin ^{-1} x$ and $x \neq 0$, then $8 x^2+1=$

Match the functions given in List I with their relevant characteristics from List II.

List I	List II
(A) sinh x	(I) Domains is (-1,1), even function
(B) sec hx	(II) Domain is [1,∞), neither even nor odd function
(C) tan hx	(III) Even function
(D) cosec h⁻¹x	(IV) Range is R, odd function
	(V) Range is (-1,1), odd function

The correct answer is

In a $\triangle A B C$, if $\tan \frac{A}{2}: \tan \frac{B}{2}: \tan \frac{C}{2}=15: 10: 6$, then $\frac{a}{b-c}=$

In a $\triangle A B C, \frac{a\left(r_1+r_2 r_3\right)}{r_1-r+r_2+r_3}=$