Question

tan inverse 2/11+tan inverse 7/24= tan inverse 1/2

Answer 1

$tan ^{ - 1} (2 \div 11) + tan ^{ - 1} (7 \div 24) = tan ^{ - 1} ((2 \div 11 \: + 7 \div 24) \div (1 - (2 \div 11)(7 \div 24))) \\ = tan ^{ - 1} (1 \div 2)$
this is your answer

Answer 2

${ \blue{ \tan {}^{ - 1} \frac{2}{11} + \tan {}^{ - 1} \frac{7}{24} = \tan {}^{ - 1} \frac{1}{2} }}$

LHS,

$\tan {}^{ - 1} \frac{2}{11} + \tan {}^{ - 1} \frac{7}{24} \\{ \green{ We \: know \: that,}}$

${\boxed{\tan {}^{ - 1} x + \tan {}^{ - 1} y = \tan {}^{ - 1} \frac{x + y}{1 - xy}}}$

$= \tan {}^{ - 1} \frac{ \frac{2}{11} + \frac{7}{24} }{1 - \frac{2}{11} \times \frac{7}{24} } \\ = \tan {}^{ - 1} \frac{48 + 77}{11 \times 24 - 14} \\ = \tan {}^{ - 1} \frac{125}{250} \\ = { \tan }^{ - 1} \frac{1}{2}$

=RHS.

________________Proved....