If A = tan11°. tan29°, B = 2cot61°. cot79° then -

Solution (By Examveda Team)

$$\eqalign{ & \Leftrightarrow \frac{{\text{A}}}{{\text{B}}} = \frac{{{\text{tan1}}{{\text{1}}^ \circ }{\text{.tan2}}{{\text{9}}^ \circ }}}{{{\text{2cot}}{{61}^ \circ }.\cot {{79}^ \circ }}} \cr & \Leftrightarrow \frac{{\text{A}}}{{\text{B}}} = \frac{{{\text{tan1}}{{\text{1}}^ \circ }{\text{.tan2}}{{\text{9}}^ \circ }}}{{{\text{2}}\left[ {{\text{cot}}\left( {{{90}^ \circ } - {{29}^ \circ }} \right).\cot \left( {{{90}^ \circ } - {{11}^ \circ }} \right)} \right]}} \cr & \Leftrightarrow \frac{{\text{A}}}{{\text{B}}} = \frac{{{\text{tan1}}{{\text{1}}^ \circ }{\text{.tan2}}{{\text{9}}^ \circ }}}{{{\text{2tan1}}{{\text{1}}^ \circ }.tan{{29}^ \circ }}} \cr & \Leftrightarrow \frac{{\text{A}}}{{\text{B}}} = \frac{1}{2} \cr & \Leftrightarrow 2{\text{A}} = {\text{B}} \cr} $$