Question

tan inverse 1/5+tan inverse 1/7+tan inverse 1/3+tan inverse 1/8=

Answer 1

tan inverse 1/5 + tan inverse 1/7 + tan inverse 1/3 + tan inverse 1/8 = π/4

Answer 2

${tan}^{ - 1} \frac{1}{5} + {tan}^{ - 1} \frac{1}{7} + {tan}^{ - 1} \frac{1}{3} + {tan}^{ - 1} \frac{1}{8} \\ \\ = {tan}^{ - 1} ( \frac{ \frac{1}{5} + \frac{1}{7} }{1 - \frac{1}{5} . \frac{1}{7} } ) + {tan}^{ - 1} ( \frac{ \frac{1}{3} + \frac{1}{ 8 } }{1 - \frac{1}{3}. \frac{1}{8} } ) \\ \\ = {tan}^{ - 1} ( \frac{7 + 5}{35 - 1} ) + {tan}^{ - 1} ( \frac{8 + 3}{24 - 1} ) \\ \\ = {tan}^{ - 1} ( \frac{12}{34} ) + {tan}^{ - 1} ( \frac{11}{23} ) \\ \\ = {tan}^{ - 1} \frac{6}{17} + {tan}^{ - 1} \frac{11}{23} \\ \\ = {tan}^{ - 1} ( \frac{ \frac{6}{17} + \frac{11}{23} }{1 - \frac{6}{17} . \frac{11}{23} } ) \\ \\ = {tan}^{ - 1} ( \frac{138 + 187}{391 - 66} ) \\ \\ = {tan}^{ - 1} ( \frac{325}{325} ) \\ \\ = {tan}^{ - 1} 1 \\ \\ = \frac{\pi}{4}$