Question

show that tan^-1 1\2 +tan^-1 2/11
=tan^-1 3/4 ?​

Answer 1

By property 5(i),we have

$\sf\red{LHS = { tan }^{ - 1} \frac{1}{2} + {tan}^{ - 1} \frac{2}{11} = {tan}^{ - 1} \frac{ \frac{1}{2} + \frac{2}{11} }{1 - \frac{1}{2} \times \frac{2}{11} } = {tan}^{ - 1} \frac{15}{20} = {tan}^{ - 1} \frac{3}{4} = RHS}$