QJEEAdv06Ma3556: JEE Advanced 2006 Mathematics - Class 12 JEEAdv06Ma3556 Solution: Match the following Column (A) then tan (B) Sides of a triangle …

Column $I$

(A) $\sum\limits_{i = 1}^\infty {{{\tan }^{ - 1}}\left( {{1 \over {2{i^2}}}} \right) = t,}$ then tan $t=$

(B) Sides $a, b, c$ of a triangle $ABC$ are in $AP$ and
$\cos {\theta _1} = {a \over {b + c}},\,\cos {\theta _2} = {b \over {a + c}},\cos {\theta _3} = {c \over {a + b}},$
then ${\tan ^2}\left( {{{{\theta _1}} \over 2}} \right) + {\tan ^2}\left( {{{{\theta _3}} \over 2}} \right) =$

(C) A line is perpendicular to $x + 2y + 2z = 0$ and
passes through $(0, 1, 0)$ . The perpendicular distance of this line from the origin is

Column $II$

(p) $1$

(q) ${{\sqrt 5 } \over 3}$

(r) ${2 \over 3}$