Question

If tan A = 4 /3, tanB = 1/ 7,then A + B =

Answer 1

$Given \:tan A = \frac{4}{3} \:and \\ tan B = \frac{1}{7}$

$We \:know \:that ,$

$\boxed { \pink { tan (A+B) = \frac{tan A + tan B }{1 - tan A \times tan B } }}$

$tan (A+B) = \frac{ \frac{4}{3} + \frac{1}{7}}{1 - \frac{4}{3} \times \frac{1}{7}} \\= \frac{ \frac{28+3}{21}}{ \frac{21-4}{21}} \\= \frac{31}{17}$

$\implies tan ( A + B ) = \frac{31}{17}$

$\implies A + B = tan^{-1} \: \frac{31}{17}$

Therefore.,

$\red { Value \: of \: A + B}\green { = tan^{-1} \: \frac{31}{17} }$

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